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Relevant bibliographies by topics / Algebraic Coding Theory

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Academic literature on the topic 'Algebraic Coding Theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Algebraic Coding Theory"

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SAKATA, Shojiro. "Algebraic Coding Theory." IEICE ESS Fundamentals Review 1, no. 3 (2008): 3_44–3_57. http://dx.doi.org/10.1587/essfr.1.3_44.

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MATSUI, Hajime. "Algebraic Methods in Coding Theory." IEICE ESS Fundamentals Review 8, no. 3 (2015): 151–61. http://dx.doi.org/10.1587/essfr.8.151.

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Wood, Jay A. "Spinor groups and algebraic coding theory." Journal of Combinatorial Theory, Series A 51, no. 2 (July 1989): 277–313. http://dx.doi.org/10.1016/0097-3165(89)90053-8.

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Campillo, Antonio, Patrick Fitzpatrick, Edgar Martínez-Moro, and Ruud Pellikaan. "Special issue algebraic coding theory and applications." Journal of Symbolic Computation 45, no. 7 (July 2010): 721–22. http://dx.doi.org/10.1016/j.jsc.2010.03.006.

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Hirschfeld, J. W. P. "INTRODUCTION TO CODING THEORY AND ALGEBRAIC GEOMETRY." Bulletin of the London Mathematical Society 23, no. 5 (September 1991): 498–500. http://dx.doi.org/10.1112/blms/23.5.498.

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Yang, Guomin, Chik How Tan, Yi Mu, Willy Susilo, and Duncan S. Wong. "Identity based identification from algebraic coding theory." Theoretical Computer Science 520 (February 2014): 51–61. http://dx.doi.org/10.1016/j.tcs.2013.09.008.

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Nagaraj, S. V. "Review of Algebraic Coding Theory Revised Edition by Elwyn Berlekamp." ACM SIGACT News 48, no. 1 (March 10, 2017): 23–26. http://dx.doi.org/10.1145/3061640.3061645.

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Astola, Jaakko. "Digital signal processing, applications to communications and algebraic coding theory." Signal Processing 23, no. 2 (May 1991): 215–16. http://dx.doi.org/10.1016/0165-1684(91)90076-u.

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Chen, Fuxing, Hui Li, Xuesong Tan, and Shuo-Yen Robert Li. "Multicast Switching Fabric Based on Network Coding and Algebraic Switching Theory." IEEE Transactions on Communications 64, no. 7 (July 2016): 2999–3010. http://dx.doi.org/10.1109/tcomm.2016.2577679.

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Couvreur, Alain. "Sums of residues on algebraic surfaces and application to coding theory." Journal of Pure and Applied Algebra 213, no. 12 (December 2009): 2201–23. http://dx.doi.org/10.1016/j.jpaa.2009.03.009.

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Dissertations / Theses on the topic "Algebraic Coding Theory"

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Cohen, D. A. "A problem in algebraic coding theory." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380002.

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Arslan, Ogul. "Some algebraic problems from coding theory." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0024938.

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Liu, Youjian. "An algebraic space-time coding theory and its applications /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488204276534358.

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Zappatore, Ilaria. "Simultaneous Rational Function Reconstruction and applications to Algebraic Coding Theory." Thesis, Montpellier, 2020. http://www.theses.fr/2020MONTS021.

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Cette thèse étudie un problème de calcul formel qui a des applications et conséquences importantes sur la théorie des codes correcteurs algébriques : la reconstruction rationnelle simultanée (RRS). En effet, une analyse rigoureuse de ce problème amène à des résultats intéressants dans ce deux domaines scientifiques.Plus précisément, la reconstruction simultanée de fractions rationnelles est le problème de la reconstruction d’un vecteur de fractions rationnelles ayant le même dénominateur étant donné ses évaluations (ou plus généralement étant donné ses restes modulo de polynômes différents). La particularité de ce problème consiste dans le fait que la contrainte du dénominateur commun réduit le nombre de points d’évaluation nécessaires pour garantir l’existence d’une solution, au prix d’une éventuelle perte d’unicité. Une des principales contributions de ce travail consiste à prouver que l’unicité est garantie pour quasiment tous les instances de ce problème.Ce résultat a été obtenu par l’élaboration des résultats et techniques précédents dérivées des applications du probleme RRS, depuis la résolution de systèmes linéaires polynomiaux jusqu’au décodage de codes Reed-Solomon entrelacés.Dans ce travail, nous avons aussi étudié et présenté une autre application du problème SRFR, concernant le problème de la construction d’algorithmes tolérants aux fautes : des algorithmes résistants aux erreurs de calcul. Ces algorithmes sont construits en introduisant une redondance et en utilisant des outils de codes correcteurs d’erreurs pour détecter et éventuellement corriger les erreurs qui se produisent pendant les calculs. Dans ce contexte d’application, nous améliorons une technique existante de tolérance aux fautes pour la résolution de systèmes linéaires polynomiaux par interpolation-évaluation, avec une attention particulière aux problème RRS correspondant
This dissertation deals with a Computer Algebra problem which has significant consequencesin Algebraic Coding Theory and Error Correcting Codes: the simultaneous rationalfunction reconstruction. Indeed, an accurate analysis of this problem leads to interestingresults in both these scientific domains.More precisely, the simultaneous rational function reconstruction is the problem of reconstructinga vector of rational functions with the same denominator given its evaluations(or more generally given its remainders modulo different polynomials). The peculiarity ofthis problem consists in the fact that the common denominator constraint reduces the numberof evaluation points needed to guarantee the existence of a solution, possibly losing theuniqueness. One of the main contribution of this work consists in the proof that uniquenessis guaranteed for almost all instances of this problem.This result was obtained by elaborating some other contributions and techniques derivedby the applications of SRFR, from the polynomial linear system solving to the decoding ofInterleaved Reed-Solomon codes.In this work, we will also study and present another application of the SRFR problem,concerning the problem of constructing fault-tolerant algorithms: algorithms resilientsto computational errors. These algorithms are constructed by introducing redundancy andusing error correcting codes tools to detect and possibly correct errors which occur duringcomputations. In this application context, we improve an existing fault-tolerant techniquefor polynomial linear system solving by interpolation-evaluation, by focusing on the SRFRproblem related to it

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Alzubi, Jafar A. "Forward error correction coding and iterative decoding using algebraic geometric theory." Thesis, Swansea University, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.582101.

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Iannone, Paola. "Automorphism groups of geometric codes." Thesis, University of East Anglia, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318091.

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Barelli, Elise. "On the security of short McEliece keys from algebraic andalgebraic geometry codes with automorphisms." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX095/document.

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En 1978, McEliece introduit un schéma de chiffrement à clé publique issu de la théorie des codes correcteurs d’erreurs. L’idée du schéma de McEliece est d’utiliser un code correcteur dont lastructure est masquée, rendant le décodage de ce code difficile pour toute personne ne connaissant pas cette structure. Le principal défaut de ce schéma est la taille de la clé publique. Dans ce contexte, on se propose d'étudier l'utilisation de codes dont on connaît une représentation compacte, en particulier le cas de codes quais-cyclique ou quasi-dyadique. Les deux familles de codes qui nous intéressent dans cette thèse sont: la famille des codes alternants et celle des sous--codes sur un sous--corps de codes géométriques. En faisant agir un automorphisme $sigma$ sur le support et le multiplier des codes alternants, on saitqu'il est possible de construire des codes alternants quasi-cycliques. On se propose alors d'estimer la sécurité de tels codes à l'aide du textit{code invariant}. Ce sous--code du code public est constitué des mots du code strictement invariant par l'automorphisme $sigma$. On montre ici que la sécurité des codes alternants quasi-cyclique se réduit à la sécurité du code invariant. Cela est aussi valable pour les sous—codes sur un sous--corps de codes géométriques quasi-cycliques. Ce résultat nous permet de proposer une analyse de la sécurité de codes quasi-cycliques construit sur la courbe Hermitienne. En utilisant cette analyse nous proposons des clés compactes pour la schéma de McEliece utilisant des sous-codes sur un sous-corps de codes géométriques construits sur la courbe Hermitienne. Le cas des codes alternants quasi-dyadiques est aussi en partie étudié. En utilisant le code invariant, ainsi que le textit{produit de Schur}et le textit{conducteur} de deux codes, nous avons pu mettre en évidence une attaque sur le schéma de McEliece utilisant des codes alternants quasi-dyadique de degré $2$. Cette attaque s'applique notamment au schéma proposé dans la soumission DAGS, proposé dans le contexte de l'appel du NIST pour la cryptographie post-quantique
In 1978, McEliece introduce a new public key encryption scheme coming from errors correcting codes theory. The idea is to use an error correcting code whose structure would be hidden, making it impossible to decode a message for anyone who do not know a specific decoding algorithm for the chosen code. The McEliece scheme has some advantages, encryption and decryption are very fast and it is a good candidate for public-key cryptography in the context of quantum computer. The main constraint is that the public key is too large compared to other actual public-key cryptosystems. In this context, we propose to study the using of some quasi-cyclic or quasi-dyadic codes. In this thesis, the two families of interest are: the family of alternant codes and the family of subfield subcode of algebraic geometry codes. We can construct quasi-cyclic alternant codes using an automorphism which acts on the support and the multiplier of the code. In order to estimate the securtiy of these QC codes we study the em{invariant code}. This invariant code is a smaller code derived from the public key. Actually the invariant code is exactly the subcode of code words fixed by the automorphism $sigma$. We show that it is possible to reduce the key-recovery problem on the original quasi-cyclic code to the same problem on the invariant code. This is also true in the case of QC algebraic geometry codes. This result permits us to propose a security analysis of QC codes coming from the Hermitian curve. Moreover, we propose compact key for the McEliece scheme using subfield subcode of AG codes on the Hermitian curve. The case of quasi-dyadic alternant code is also studied. Using the invariant code, with the em{Schur product} and the em{conductor} of two codes, we show weaknesses on the scheme using QD alternant codes with extension degree 2. In the case of the submission DAGS, proposed in the context of NIST competition, an attack exploiting these weakness permits to recover the secret key in few minutes for some proposed parameters

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Jansen, Anthony Robert 1973. "Encoding and parsing of algebraic expressions by experienced users of mathematics." Monash University, School of Computer Science and Software Engineering, 2002. http://arrow.monash.edu.au/hdl/1959.1/8059.

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Peixoto, Rafael 1983. "Funções pesos fracos sobre variedades algébricas." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307079.

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Orientadores: Fernando Eduardo Torres Orihuela, Cícero Fernandes de Carvalho
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-19T03:11:40Z (GMT). No. of bitstreams: 1 Peixoto_Rafael_D.pdf: 876847 bytes, checksum: ae0f5d0ea0f2c3e3d550bc60eb1ac66a (MD5) Previous issue date: 2011
Resumo: Definidas sobre uma F-álgebra, os conceitos de função peso e função peso fraco foram introduzidos de forma a simplificar a teoria dos códigos corretores de erros que utilizam ferramentas da geometria algébrica. Porém, todos os códigos suportados por estes conceitos estão intimamente ligados à códigos provenientes de curvas algébricas, ou seja, os códigos geométricos de Goppa. Uma modificação da noção de função peso foi apresentada permitindo assim construir códigos lineares sobre variedades algébricas. Nesta tese, apresentamos uma generalização da teoria de funções pesos fracos que possibilitou a construção de códigos sobre variedades de dimensão arbitrária. Determinamos uma cota para a distância mínima destes códigos, e finalmente, apresentamos uma caracterização tanto para as álgebras munidas de funções pesos quanto para as álgebras munidas de um conjunto especial de funções pesos fracos
Abstract: Defined on a F-algebra, the concepts of weight and near weight function were introduced to simplify the theory of error correcting codes using tools from algebraic geometry. However, all codes supported by these theories are geometric Goppa codes. The concept of weight function was generalized and used to construct linear codes on algebraic varieties. In this thesis, we present a generalization of near weights theory able to construct codes on higher dimensional varieties, and we define a formula for the minimum distance of such codes. Finally, we characterize the algebras with a weight function and the algebras admitting a special set of two near weight functions
Doutorado
Matematica
Doutor em Matemática

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Melo, Nolmar. "Codigos geometricos de Goppa via metodos elementares." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306316.

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Orientadores: Paulo Roberto Brumatti, Fernando Eduardo Torres Orihuela
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-05T23:44:44Z (GMT). No. of bitstreams: 1 Melo_Nolmar_M.pdf: 705654 bytes, checksum: b8ecfe0cc3ffd2dd2f63bc813a9c4a8d (MD5) Previous issue date: 2006
Resumo: O objetivo central desta dissertação foi o de apresentar os Códigos Geométricos de Goppa via métodos elementares que foram introduzidos por J. H. van Lint, R. Pellikaan e T. Hfhold por volta de 1998. Numa primeira parte da dissertação são apresentados os conceitos fundamentais sobre corpos de funções racionais de uma curva algébrica na direção de se definir os códigos de Goppa de maneira clássica, neste estudo nos baseamos principalmente no livro ¿Algebraic Function Fields and Codes¿ de H. Stichtenoth. A segunda parte inicia-se com a introdução dos conceitos de funções peso, grau e ordem que são fundamentais para o estudo dos Códigos de Goppa via métodos elementares de álgebra linear e de semigrupos, tal estudo foi baseado em ¿Algebraic geometry codes¿ de J. H. van Lint, R. Pellikaan e T. Hfhold.A dissertação termina com a apresentação de exemplos que ilustram os métodos elementares que nos referimos acima
Abstract: The central objective of this dissertation was to present the Goppa Geometry Codes via elementary methods which were introduced by J. H. van Lint, R. Pellikaan and T. Hfhold about 1998. On the first past of such dissertation are presented the fundamental concepts about fields of rational functions of an algebraic curve in the direction as to define the Goppa Codes on a classical manner. In this study we based ourselves mainly on the book ¿Algebraic Function Fields and Codes¿ of H. Stichtenoth. The second part is initiated with an introduction about the functions weight, degree and order which are fundamental for the study of the Goppa Codes throught elementary methods of linear algebra and of semigroups and such study was based on ¿Algebraic Geometry Codes¿ of J. h. van Lint, R. Pellikaan and T. Hfhold. The dissertation ends up with a presentation of examples which illustrate the elementary methods that we have referred to above
Mestrado
Algebra
Mestre em Matemática

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Books on the topic "Algebraic Coding Theory"

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Vermani, L. R. Elements of Algebraic Coding Theory. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-7268-2.

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Stichtenoth, Henning, and Michael A. Tsfasman, eds. Coding Theory and Algebraic Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0087986.

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K, Kythe Prem, ed. Algebraic and stochastic coding theory. Boca Raton: CRC Press, 2012.

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Tsfasman, M. A. Algebraic-geometric codes. Dordrecht: Kluwer Academic Publishers, 1991.

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Lint, J. H. Van. Introduction to coding theory and algebraic geometry. Basel: Birkhäuser, 1988.

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Lint, Jacobus Hendricus van. Introduction to coding theory and algebraic geometry. Basel: Birkhäuser Verlag, 1988.

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1963-, Xing Chaoping, ed. Algebraic geometry in coding theory and cryptography. Princeton: Princeton University Press, 2009.

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van Lint, Jacobus H., and Gerard van der Geer. Introduction to Coding Theory and Algebraic Geometry. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9286-5.

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Dougherty, Steven T. Algebraic Coding Theory Over Finite Commutative Rings. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59806-2.

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Howe, Everett W., Kristin E. Lauter, and Judy L. Walker, eds. Algebraic Geometry for Coding Theory and Cryptography. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63931-4.

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Book chapters on the topic "Algebraic Coding Theory"

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Biggs, Norman L. "Algebraic coding theory." In Springer Undergraduate Mathematics Series, 1–22. London: Springer London, 2008. http://dx.doi.org/10.1007/978-1-84800-273-9_9.

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Mullen, Gary, and Carl Mummert. "Algebraic coding theory." In The Student Mathematical Library, 79–108. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/stml/041/03.

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Cox, David, John Little, and Donal O’Shea. "Algebraic Coding Theory." In Using Algebraic Geometry, 407–67. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4757-6911-1_9.

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Van Lint, Jacobus H. "Algebraic Geometric Codes." In Coding Theory and Design Theory, 137–62. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4613-8994-1_12.

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van Lint, J. H. "Algebraic Geometry Codes." In Introduction to Coding Theory, 148–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-58575-3_10.

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van Lint, J. H. "Asymptotically Good Algebraic Codes." In Introduction to Coding Theory, 127–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-00174-5_9.

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van Lint, J. H. "Asymptotically Good Algebraic Codes." In Introduction to Coding Theory, 167–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-58575-3_11.

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Shparlinski, Igor E. "Coding Theory and Algebraic Curves." In Finite Fields: Theory and Computation, 149–213. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9239-0_7.

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Chirikjian, Gregory S. "Algebraic and Geometric Coding Theory." In Stochastic Models, Information Theory, and Lie Groups, Volume 2, 313–36. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-4944-9_9.

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Heise, W. "Topics in Algebraic Coding Theory." In Geometries, Codes and Cryptography, 77–99. Vienna: Springer Vienna, 1990. http://dx.doi.org/10.1007/978-3-7091-2838-1_3.

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Conference papers on the topic "Algebraic Coding Theory"

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"Sessions: algebraic coding." In 1988 IEEE International Symposium on Information Theory. IEEE, 1988. http://dx.doi.org/10.1109/isit.1988.22243.

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Sudan, Madhu. "Algebraic algorithms and coding theory." In the twenty-first international symposium. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1390768.1390816.

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Daskalov, Rumen, and Elena Metodieva. "Three new large (n, r) arcs in PG(2,31)." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383380.

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Boumova, Silvia, Tedis Ramaj, and Maya Stoyanova. "On Covering Radius of Orthogonal Arrays." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383398.

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Kunz, Johannes, Julian Renner, Georg Maringer, Thomas Schamberger, and Antonia Wachter-Zeh. "On Software Implementation of Gabidulin Decoders." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383242.

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Kasparian, Azniv. "Riemann-Roch Theorem and Mac Williams identities for an additive code with respect to a saturated lattice." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383243.

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Markov, Miroslav, and Yuri Borissov. "Point-Counting on Elliptic Curves Belonging to One Prominent Family: Revisited." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383390.

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Verma, Ram Krishna, Om Prakash, and Ashutosh Singh. "Quantum codes from skew constacyclic codes over Fp m + vFp m + v2Fp m." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383402.

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Honold, Thomas, Michael Kiermaier, and Ivan Landjev. "New upper bounds on the maximal size of an arc in a projective Hjelmslev plane." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383345.

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"ACCT 2020 Table of Content." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383388.

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Reports on the topic "Algebraic Coding Theory"

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Xia, Xiang-Gen. Space-Time Coding Using Algebraic Number Theory for Broadband Wireless Communications. Fort Belvoir, VA: Defense Technical Information Center, May 2008. http://dx.doi.org/10.21236/ada483791.

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