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Data publikacji: 4 czerwca 2021
Data aktualizacji: 30 lipca 2024

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1

Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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<p>This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions
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2

Pizzato, Marco. "Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements." Doctoral thesis, Università degli studi di Trento, 2013. https://hdl.handle.net/11572/367913.

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In this thesis we consider some problems concerning polynomials over finite fields. The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. Next, we consider transformations of irreducible polynomials by quadratic and cubic maps and study the irreducibility of the polynomials obtained. Finally, starting from PN functions and monomials, we generalize this concept, introducing k-PN monomials and classifying them for small values of k and for fields of order p, p^2 and p^4.
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3

Prešern, Mateja. "Existence problems of primitive polynomials over finite fields." Connect to e-thesis. Move to record for print version, 2007. http://theses.gla.ac.uk/50/.

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Thesis (Ph.D.) - University of Glasgow, 2007.<br>Ph.D. thesis submitted to the Department of Mathematics, Faculty of Information and Mathematical Sciences, University of Glasgow, 2007. Includes bibliographical references.
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4

GOMEZ-CALDERON, JAVIER. "POLYNOMIALS WITH SMALL VALUE SET OVER FINITE FIELDS." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183933.

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Let K(q) be the finite field with q elements and characteristic p. Let f(x) be a monic polynomial of degree d with coefficients in K(q). Let C(f) denote the number of distinct values of f(x) as x ranges over K(q). It is easy to show that C(f) ≤ [|(q - 1)/d|] + 1. Now, there is a characterization of polynomials of degree d < √q for which C(f) = [|(q - 1)/d|] +1. The main object of this work is to give a characterization for polynomials of degree d < ⁴√q for which C(f) < 2q/d. Using two well known theorems: Hurwitz genus formula and Andre Weil's theorem, the Riemann Hypothesis for Algebraic Fun
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5

Pizzato, Marco. "Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements." Doctoral thesis, University of Trento, 2013. http://eprints-phd.biblio.unitn.it/1121/1/PizzatoPhDThesisbis.pdf.

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In this thesis we consider some problems concerning polynomials over finite fields. The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. Next, we consider transformations of irreducible polynomials by quadratic and cubic maps and study the irreducibility of the polynomials obtained. Finally, starting from PN functions and monomials, we generalize this concept, introducing k-PN monomials and classifying them for small values of k and for fields of order p, p^2 and p^4.
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6

Akleylek, Sedat. "On The Representation Of Finite Fields." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612727/index.pdf.

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The representation of field elements has a great impact on the performance of the finite field arithmetic. In this thesis, we give modified version of redundant representation which works for any finite fields of arbitrary characteristics to design arithmetic circuits with small complexity. Using our modified redundant representation, we improve many of the complexity values. We then propose new representations as an alternative way to represent finite fields of characteristic two by using Charlier and Hermite polynomials. We show that multiplication in these representations can be achieved wi
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7

Jogia, Danesh Michael Mathematics &amp Statistics Faculty of Science UNSW. "Algebraic aspects of integrability and reversibility in maps." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/40947.

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We study the cause of the signature over finite fields of integrability in two dimensional discrete dynamical systems by using theory from algebraic geometry. In particular the theory of elliptic curves is used to prove the major result of the thesis: that all birational maps that preserve an elliptic curve necessarily act on that elliptic curve as addition under the associated group law. Our result generalises special cases previously given in the literature. We apply this theorem to the specific cases when the ground fields are finite fields of prime order and the function field $mathbb{C}(t
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8

Park, Hong Goo. "Polynomial Isomorphisms of Cayley Objects Over a Finite Field." Thesis, University of North Texas, 1989. https://digital.library.unt.edu/ark:/67531/metadc331144/.

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In this dissertation the Bays-Lambossy theorem is generalized to GF(pn). The Bays-Lambossy theorem states that if two Cayley objects each based on GF(p) are isomorphic then they are isomorphic by a multiplier map. We use this characterization to show that under certain conditions two isomorphic Cayley objects over GF(pn) must be isomorphic by a function on GF(pn) of a particular type.
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9

Baktir, Selcuk. "Efficient algorithms for finite fields, with applications in elliptic curve cryptography." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0501103-132249.

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Thesis (M.S.)--Worcester Polytechnic Institute.<br>Keywords: multiplication; OTF; optimal extension fields; finite fields; optimal tower fields; cryptography; OEF; inversion; finite field arithmetic; elliptic curve cryptography. Includes bibliographical references (p. 50-52).
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10

Veliz-Cuba, Alan A. "The Algebra of Systems Biology." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/28240.

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In order to understand biochemical networks we need to know not only how their parts work but also how they interact with each other. The goal of systems biology is to look at biological systems as a whole to understand how interactions of the parts can give rise to complex dynamics. In order to do this efficiently, new techniques have to be developed. This work shows how tools from mathematics are suitable to study problems in systems biology such as modeling, dynamics prediction, reverse engineering and many others. The advantage of using mathematical tools is that there is a large num
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11

Grout, Jason Nicholas. "The Minimum Rank Problem Over Finite Fields." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1995.pdf.

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12

Vargas, Jorge Ivan. "A characterization of pseudo-orders in the ring Zn." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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13

Hart, Derrick. "Explorations of geometric combinatorics in vector spaces over finite fields." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5585.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 8, 2009) Vita. Includes bibliographical references.
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14

Psioda, Matthew. "An examination of the structure of extension families of irreducible polynomials over finite fields /." Electronic version (PDF), 2006. http://dl.uncw.edu/etd/2006/psiodam/matthewpsioda.pdf.

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15

Rousseau, Édouard. "Efficient arithmetic of finite field extension." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAT013.

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Les corps finis sont omniprésents en cryptographie et en théorie des codes, deux domaines de première importance dans les communications modernes. Ainsi, il est crucial de représenter les corps finis et d’y faire des calculs de la façon la plus efficace possible. Dans cette thèse, nous travaillons sur l’arithmétique des extensions de corps finis, de deux manières différentes et indépendantes.Dans la première partie, nous étudions l’arithmétique d’une unique extension de corps fini F_{p^k}. Lorsqu’on souhaite estimer la complexité d’un algorithme dans une extension, on compte souvent les opérat
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16

Cazavan, Jilyana. "Algorithms for finite field arithmetic and decoding of Reed-Solomon codes." Thesis, Queensland University of Technology, 1991. https://eprints.qut.edu.au/35965/1/35965_Cazavan_1991.pdf.

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This thesis contains a description of various algorithms for arithmetic in the finite field GF(pm) along with decoding algorithms for Reed-Solomon codes. Emphasis in this thesis is placed on algorithms which require a minimal number of GF(pm) operations yet may be quite complex. Some known methods to do arithmetic in GF(pm) are summarized in chapter 2. Methods are also derived for the determination of the nth roots of elements in GF(pm) when n = p8 -pt for positive integers sand t, and n = 3 for GF(2m). In chapter 3, the Itoh-Tsujii algorithm which calculates the multiplicative inverse of an
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17

Culbert, Craig W. "Spreads of three-dimensional and five-dimensional finite projective geometries." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 101 p, 2009. http://proquest.umi.com/pqdweb?did=1891555371&sid=3&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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18

Cam, Vural. "Drinfeld Modular Curves With Many Rational Points Over Finite Fields." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613118/index.pdf.

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In our study Fq denotes the finite field with q elements. It is interesting to construct curves of given genus over Fq with many Fq -rational points. Drinfeld modular curves can be used to construct that kind of curves over Fq . In this study we will use reductions of the Drinfeld modular curves X_{0} (n) to obtain curves over finite fields with many rational points. The main idea is to divide the Drinfeld modular curves by an Atkin-Lehner involution which has many fixed points to obtain a quotient with a better #{rational points} /genus ratio. If we divide the Drinfeld modular curve X_{0} (n)
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19

Kurtaran, Ozbudak Elif. "Results On Some Authentication Codes." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/2/12610350/index.pdf.

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In this thesis we study a class of authentication codes with secrecy. We obtain the maximum success probability of the impersonation attack and the maximum success probability of the substitution attack on these authentication codes with secrecy. Moreover we determine the level of secrecy provided by these authentication codes. Our methods are based on the theory of algebraic function fields over finite fields. We study a certain class of algebraic function fields over finite fields related to this class of authentication codes. We also determine the number of rational places of this class of
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20

McCulloch, Catherine Margaret. "Discrete logarithm problem over finite prime fields." Thesis, Queensland University of Technology, 1998. https://eprints.qut.edu.au/36976/1/36976_McCulloch_1988.pdf.

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Difficulty in solving the discrete logarithm problem has led to its use in key exchange, public key cryptography and digital signatures. To measure the security of these algorithms, it is necessary to evaluate the methods currently available for attack. Although the applications of the discrete logarithm problem can be implemented in a variety of different groups, only implementations over multiplicative integers modulo a large prime p are considered. The object of this work is to review the current methods of solving the discrete logarithm problem - key exhaustion, Shanks' baby-step giant-st
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21

Angulo, Rigo Julian Osorio. "Criptografia de curvas elípticas." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/6976.

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22

Reis, Júlio César dos 1979. "Graduações e identidades graduadas para álgebras de matrizes." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306363.

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Orientador: Plamen Emilov Kochloukov<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T11:39:36Z (GMT). No. of bitstreams: 1 Reis_JulioCesardos_D.pdf: 2452563 bytes, checksum: 63f8b1d463a36f74d57c1d71769dc9ae (MD5) Previous issue date: 2012<br>Resumo: Na presente tese, fornecemos bases das identidades polinomiais graduadas de...Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital<br>Abstract: In this PhD thesis we give bases of the graded polyn
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23

Ranorovelonalohotsy, Marie Brilland Yann. "Riemann hypothesis for the zeta function of a function field over a finite field." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85713.

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24

Lingenbrink, David Alan Jr. "A New Subgroup Chain for the Finite Affine Group." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/55.

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The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.
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25

Castilho, Tiago Nunes 1983. "Sobre o numero de pontos racionais de curvas sobre corpos finitos." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307074.

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Orientador: Fernando Eduardo Torres Orihuela<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-10T15:12:25Z (GMT). No. of bitstreams: 1 Castilho_TiagoNunes_M.pdf: 813127 bytes, checksum: 313e9951b003dcd0e0876813659d7050 (MD5) Previous issue date: 2008<br>Resumo: Nesta dissertacao estudamos cotas para o numero de pontos racionais de curvas definidas sobre corpos finitos tendo como ponto de partida a teoria de Stohr-Voloch<br>Abstract: In this work we study upper bounds on the numbe
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26

Lötter, Ernest C. "On towers of function fields over finite fields /." Link to the online version, 2007. http://hdl.handle.net/10019.1/1283.

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Lotter, Ernest Christiaan. "On towers of function fields over finite fields." Thesis, Stellenbosch : University of Stellenbosch, 2007. http://hdl.handle.net/10019.1/1283.

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Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007.<br>Explicit towers of algebraic function fields over finite fields are studied by considering their ramification behaviour and complete splitting. While the majority of towers in the literature are recursively defined by a single defining equation in variable separated form at each step, we consider towers which may have different defining equations at each step and with arbitrary defining polynomials. The ramification and completely splitting loci are analysed by directed graphs with irreducible polynomials as vert
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28

Negreiros, Diogo Bruno Fernandes 1983. "Formas quadráticas, pesos de Hamming generalizados e curvas algébricas." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306293.

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Orientador: Paulo Roberto Brumatti<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-18T19:35:36Z (GMT). No. of bitstreams: 1 Negreiros_DiogoBrunoFernandes_M.pdf: 5674415 bytes, checksum: bdd28225d3cc5505f91fd61e797f2794 (MD5) Previous issue date: 2011<br>Resumo: Este texto tem como objetivo o estudo de um tipo de código que possui relações com as teorias de curvas algébricas e de formas quadráticas. Começaremos introduzindo as definições e resultados sobre as três teorias que ser
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29

Marín, Oscar Jhoan Palacio. "Códigos Hermitianos Generalizados." Universidade Federal de Juiz de Fora (UFJF), 2016. https://repositorio.ufjf.br/jspui/handle/ufjf/2349.

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Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-15T15:24:51Z No. of bitstreams: 1 oscarjhoanpalaciomarin.pdf: 723203 bytes, checksum: d8ac71f1e1162340ce21f336196d0070 (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-16T13:02:45Z (GMT) No. of bitstreams: 1 oscarjhoanpalaciomarin.pdf: 723203 bytes, checksum: d8ac71f1e1162340ce21f336196d0070 (MD5)<br>Made available in DSpace on 2016-08-16T13:02:45Z (GMT). No. of bitstreams: 1 oscarjhoanpalaciomarin.pdf: 723203 bytes, checksum: d8ac71f1e1162340ce21f336196d0070
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Ganz, Jürg Werner. "Algebraic complexity in finite fields /." Zürich, 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10867.

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31

Ribeiro, Beatriz Casulari da Motta 1984. "O arco associado a uma generalização da curva Hermitiana." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307081.

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Orientadores: Fernando Eduardo Torres Orihuela, Herivelto Martins Borges Filho<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-19T05:54:38Z (GMT). No. of bitstreams: 1 Ribeiro_BeatrizCasularidaMotta_D.pdf: 51476410 bytes, checksum: 46cb0c7a6206a5f0683b23a73ff3938e (MD5) Previous issue date: 2011<br>Resumo: Obtemos novos arcos completos associados ao conjunto de pontos racionais de uma certa generalização da curva Hermitiana que é Frobenius não-clássica. A construção está relacionada a
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32

Voloch, J. F. "Curves over finite fields." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355283.

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33

Hua, Jiuzhao Mathematics &amp Statistics Faculty of Science UNSW. "Representations of quivers over finite fields." Awarded by:University of New South Wales. Mathematics & Statistics, 1998. http://handle.unsw.edu.au/1959.4/40405.

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The main purpose of this thesis is to obtain surprising identities by counting the representations of quivers over finite fields. A classical result states that the dimension vectors of the absolutely indecomposable representations of a quiver ?? are in one-to-one correspondence with the positive roots of a root system ??, which is infinite in general. For a given dimension vector ?? ??? ??+, the number A??(??, q), which counts the isomorphism classes of the absolutely indecomposable representations of ?? of dimension ?? over the finite field Fq, turns out to be a polynomial in q with integer
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34

Lindqvist, Anders. "On four-dimensional unital division algebras over finite fields." Thesis, Uppsala universitet, Algebra och geometri, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-254656.

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35

Berardini, Elena. "Algebraic geometry codes from surfaces over finite fields." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0170.

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Nous proposons, dans cette thèse, une étude théorique des codes géométriques algébriques construits à partir de surfaces définies sur les corps finis. Nous prouvons des bornes inférieures pour la distance minimale des codes sur des surfaces dont le diviseur canonique est soit nef soit anti-strictement nef et sur des surfaces sans courbes irréductibles de petit genre. Nous améliorons ces bornes inférieures dans le cas des surfaces dont le nombre de Picard arithmétique est égal à un, des surfaces sans courbes de petite auto-intersection et des surfaces fibrées. Ensuite, nous appliquons ces borne
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36

Panario, Rodriguez Daniel Nelson. "Combinatorial and algebraic aspects of polynomials over finite fields." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0016/NQ28297.pdf.

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37

Amorós, Carafí Laia. "Images of Galois representations and p-adic models of Shimura curves." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/471452.

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The Langlands program is a vast and unifying network of conjectures that connect the world of automorphic representations of reductive algebraic groups and the world of Galois representations. These conjectures associate an automorphic representation of a reductive algebraic group to every n-dimensional representation of a Galois group, and the other way around: they attach a Galois representation to any automorphic representation of a reductive algebraic group. Moreover, these correspondences are done in such a way that the automorphic L-functions attached to the two objects coincide. T
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Ducet, Virgile. "Construction of algebraic curves with many rational points over finite fields." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4043/document.

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L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellement en deux cas : lorsque le genre est petit (typiquement g&lt;=50), et lorsqu'il tend vers l'infini. Nous consacrons une partie de cette thèse à chacun de ces cas. Dans la première partie de notre étude nous expliquons comment calculer l'équation de n'importe quel revêtement abélien d'une courbe définie sur un corps fini. Nous utilisons pour cela la théorie explicite du corps de classe fournie par les extensions de Kummer et d'Artin-Schreier-Witt. Nous détaillons également un algorithme pour la r
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Aleem, Hosam Abdel. "An algebraic approach to modelling the regulation of gene expression." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/an-algebraic-approach-to-modelling-the-regulation-of-gene-expression(d5d400b5-690e-4f32-9fd6-c80e4db455f3).html.

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Biotechnology is witnessing a remarkable growth evident both in the types of new products and in the innovative new processes developed. More efficient process design, optimisation and troubleshooting can be achieved through a better understanding of the underlying biological processes inside the cell; a key one of which is the regulation of gene expression. For engineers such understanding is attained through mathematical modelling, and the most commonly used models of gene expression regulation are those based on differential equations, as they give quantitative results. However, those resul
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Wesche, Morten Verfasser], and Bettina [Akademischer Betreuer] [Eick. "Enumeration of class 2 associative algebras over finite fields / Morten Wesche ; Betreuer: Bettina Eick." Braunschweig : Technische Universität Braunschweig, 2018. http://d-nb.info/1175814725/34.

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Marseglia, Stefano. "Isomorphism classes of abelian varieties over finite fields." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-130316.

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Deligne and Howe described polarized abelian varieties over finite fields in terms of finitely generated free Z-modules satisfying a list of easy to state axioms. In this thesis we address the problem of developing an effective algorithm to compute isomorphism classes of (principally) polarized abelian varieties over a finite field, together with their automorphism groups. Performing such computations requires the knowledge of the ideal classes (both invertible and non-invertible) of certain orders in number fields. Hence we describe a method to compute the ideal class monoid of an order and w
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Mohamed, Mostafa Hosni [Verfasser]. "Algebraic decoding over finite and complex fields using reliability information / Mostafa Hosni Mohamed." Ulm : Universität Ulm, 2018. http://d-nb.info/1150781041/34.

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Dang, Thanh-Hung. "Scalar complexity of Chudnovsky-type algorithms of multiplication in finite fields." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0131.

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L’algorithme de type évaluation-interpolation sur des courbes algébriques, introduit par D.V et G.V Chudnovsky en 1987, est à la base des techniques algorithmiques fournissant actuellement les meilleures bornes de la complexité bilinéaire de la multiplication dans les corps finis. En particulier, ces algorithmes sont connus pour avoir asymptotiquement une complexité bilinéaire linéaire ou quasi linéaire. Mais jusqu’à présent aucun travail ne s’était attaqué à l’analyse de leur complexité scalaire. Aussi, s’intéresse-t-on dans cette thèse à la complexité scalaire de ces algorithmes. Plus précis
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Wang, Jing [Verfasser], and Istvan [Akademischer Betreuer] Heckenberger. "Finite dimensional Nichols algebras of diagonal type over fields of positive characteristic / Jing Wang. Betreuer: Istvan Heckenberger." Marburg : Philipps-Universität Marburg, 2016. http://d-nb.info/1112263594/34.

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Calderon, Federico B. [Verfasser], and Christopher [Akademischer Betreuer] Deninger. "Counting singular points of algebraic varieties over finite fields / Federico B. Calderon ; Betreuer: Christopher Deninger." Münster : Universitäts- und Landesbibliothek Münster, 2020. http://d-nb.info/1212933583/34.

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Qian, Liqin. "Contributions to the theory of algebraic coding on finite fields and rings and their applications." Electronic Thesis or Diss., Paris 8, 2022. http://www.theses.fr/2022PA080064.

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La théorie du codage algébrique sur les corps et les anneaux finis a une grande importance dans la théorie de l'information en raison de leurs diverses applications dans les schémas de partage de secrets, les graphes fortement réguliers, les codes d'authentification et de communication. Cette thèse aborde plusieurs sujets de recherche selon les orientations dans ce contexte, dont les méthodes de construction sont au cœur de nos préoccupations. Plus précisément, nous nous intéressons aux constructions de codes optimaux (ou codes asymptotiquement optimaux), aux constructions de codes linéaires à
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Alexander, Nicholas Charles. "Algebraic Tori in Cryptography." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1154.

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Communicating bits over a network is expensive. Therefore, cryptosystems that transmit as little data as possible are valuable. This thesis studies several cryptosystems that require significantly less bandwidth than conventional analogues. The systems we study, called torus-based cryptosystems, were analyzed by Karl Rubin and Alice Silverberg in 2003 [RS03]. They interpreted the XTR [LV00] and LUC [SL93] cryptosystems in terms of quotients of algebraic tori and birational parameterizations, and they also presented CEILIDH, a new torus-based cryptosystem. This thesis introduces
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Jayantha, Suranimalee Mannaperuma Herath Mudiyanselage [Verfasser], and Claus [Akademischer Betreuer] Fieker. "Linear Algebra over Finitely Generated Fields and Rings / Mannaperuma Herath Mudiyanselage Jayantha Suranimalee ; Betreuer: Claus Fieker." Kaiserslautern : Technische Universität Kaiserslautern, 2021. http://d-nb.info/1241117594/34.

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Hinkelmann, Franziska Babette. "Algebraic theory for discrete models in systems biology." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28509.

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This dissertation develops algebraic theory for discrete models in systems biology. Many discrete model types can be translated into the framework of polynomial dynamical systems (PDS), that is, time- and state-discrete dynamical systems over a finite field where the transition function for each variable is given as a polynomial. This allows for using a range of theoretical and computational tools from computer algebra, which results in a powerful computational engine for model construction, parameter estimation, and analysis methods. Formal definitions and theorems for PDS and the concept of
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ASSIS, FRANCISCO MARCOS DE. "DECODING OF ALGEBRAIC GEOMETRY CODES AND THE USE OF NEURAL NETWORKS FOR FINITE FIELD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1994. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8517@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Este trabalho propõe um algoritmo para decodificação de códigos de geometria algébrica. Usando as propriedades geométricas da curva que define um código de Goppa com distância projetada d, método permite decodificar até [d - 1/ 2] erros em palavra recebida, sem esforço computacional adicional. As curvas de F. K. Schimdt são usada para construir uma nova classe de códigos de geometria algébrica, algumas propriedades destes novos códigos são apresentadas. Redes neurais não ortodoxas do tipo feedforward e não treinadas são
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