Relevant bibliographies by topics / Algebraic geometric codes

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Algebraic geometric codes'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Algebraic geometric codes"

1

Chen, Hao. "Testing algebraic geometric codes." Science in China Series A: Mathematics 52, no. 10 (August 8, 2009): 2171–76. http://dx.doi.org/10.1007/s11425-009-0141-4.

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Chen, H., S. Ling, and C. Xing. "Quantum Codes From Concatenated Algebraic-Geometric Codes." IEEE Transactions on Information Theory 51, no. 8 (August 2005): 2915–20. http://dx.doi.org/10.1109/tit.2005.851760.

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Walker, Judy L. "Algebraic geometric codes over rings." Journal of Pure and Applied Algebra 144, no. 1 (December 1999): 91–110. http://dx.doi.org/10.1016/s0022-4049(98)00047-4.

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Lint, J. H. van. "Book Review: Algebraic-geometric codes." Bulletin of the American Mathematical Society 27, no. 2 (October 1, 1992): 306–11. http://dx.doi.org/10.1090/s0273-0979-1992-00311-7.

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Chen, Hao. "Algebraic geometric codes with applications." Frontiers of Mathematics in China 2, no. 1 (March 2007): 1–11. http://dx.doi.org/10.1007/s11464-007-0001-x.

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Sorensen, A. B. "Weighted Reed-Muller codes and algebraic-geometric codes." IEEE Transactions on Information Theory 38, no. 6 (1992): 1821–26. http://dx.doi.org/10.1109/18.165459.

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Shokrollahi, M. A., and H. Wasserman. "List decoding of algebraic-geometric codes." IEEE Transactions on Information Theory 45, no. 2 (March 1999): 432–37. http://dx.doi.org/10.1109/18.748993.

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Pellikan, R., B. Z. Shen, and G. J. M. van Wee. "Which linear codes are algebraic-geometric?" IEEE Transactions on Information Theory 37, no. 3 (May 1991): 583–602. http://dx.doi.org/10.1109/18.79915.

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Davis, Jennifer A. "Algebraic geometric codes on anticanonical surfaces." Journal of Pure and Applied Algebra 215, no. 4 (April 2011): 496–510. http://dx.doi.org/10.1016/j.jpaa.2010.06.002.

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Duursma, Iwan, Radoslav Kirov, and Seungkook Park. "Distance bounds for algebraic geometric codes." Journal of Pure and Applied Algebra 215, no. 8 (August 2011): 1863–78. http://dx.doi.org/10.1016/j.jpaa.2010.10.018.

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Dissertations / Theses on the topic "Algebraic geometric codes"

1

Guenda, Kenza. "On algebraic geometric codes and some related codes." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/2033.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2006.
The main topic of this thesis is the construction of the algebraic geometric codes (Goppa codes), and their decoding by the list-decoding, which allows one to correct beyond half of the minimum distance. We also consider the list-decoding of the Reed–Solomon codes as they are subclass of the Goppa codes, and the determination of the parameters of the non primitive BCH codes. AMS Subject Classification: 4B05, 94B15, 94B35, 94B27, 11T71, 94B65,B70. Keywords: Linear codes, cyclic codes, BCH codes, Reed–Solomon codes, list-decoding, Algebraic Geometric codes, decoding, bound on codes, error probability.
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CRISSAFF, LHAYLLA DOS SANTOS. "AN ALGEBRAIC CONSTRUCTION OF GEOMETRIC CODES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2005. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7082@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Começamos estudando uma classe particular de códigos lineares, os chamados códigos de Goppa que são obtidos calculando o valor de certas funções em pontos de Kn, onde K é um corpo finito. Apresentamos uma generalização desta construção e definimos códigos de avaliação sobre K- ágebras satisfazendo certas propriedades. Para estes códigos, descrevemos um algoritmo de decodificação e mostramos que se considerarmos os códigos de Goppa em um ponto como exemplo desta nova construção, o algoritmo corrige mais erros do que o algoritmo clássico para os códigos de Goppa.
We begin studying a certain type of linear code the so-called Goppa codes. These codes are constructed by taking the evaluation of certain functions at points in Kn, where K is a finite field. As a generalization of this construction, we introduce the so-called evaluation codes defined over K-algebras satisfying some properties. For these codes, we describe a decoding algorithm and we show that if we consider classical one-point Goppa codes as an example of the new construction, this algorithm correct more errors that the classical algorithm for Goppa codes.
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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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Johnston, Martin. "Design and implementation of algebraic-geometric codes over AWGN and fading channels." Thesis, University of Newcastle Upon Tyne, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.430341.

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Marhenke, Jörg. "On algorithms for coding and decoding algebraic-geometric codes and their implementation." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:289-vts-65822.

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Alkandari, Maryam Mohammed. "Decoding partial algebraic geometrric codes." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405512.

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Jeffs, Robert Amzi. "Convexity of Neural Codes." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/87.

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An important task in neuroscience is stimulus reconstruction: given activity in the brain, what stimulus could have caused it? We build on previous literature which uses neural codes to approach this problem mathematically. A neural code is a collection of binary vectors that record concurrent firing of neurons in the brain. We consider neural codes arising from place cells, which are neurons that track an animal's position in space. We examine algebraic objects associated to neural codes, and completely characterize a certain class of maps between these objects. Furthermore, we show that such maps have natural geometric implications related to the receptive fields of place cells. Lastly we describe several purely geometric results related to neural codes.
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Rocha, Junior Mauro Rodrigues. "Bases de Gröbner aplicadas a códigos corretores de erros." Universidade Federal de Juiz de Fora (UFJF), 2017. https://repositorio.ufjf.br/jspui/handle/ufjf/5946.

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O principal objetivo desse trabalho é estudar duas aplicações distintas das bases de Gröbner a códigos lineares. Com esse objetivo, estudamos como relacionar códigos a outras estruturas matemáticas, fazendo com que tenhamos novas ferramentas para a realização da codificação. Em especial, estudamos códigos cartesianos afins e os códigos algébrico-geométricos de Goppa.
The main objective of this work is to study two different applications of Gröbner basis to linear codes. With this purpose, we study how to relate codes to other mathematical structures, allowing us to use new tools to do the coding. In particular, we study affine cartesian codes e algebraic-geometric Goppa codes.
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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 bornes aux surfaces plongées dans P3. Une attention particulière est accordée aux codes construits à partir des surfaces abéliennes. Dans ce contexte, nous donnons une borne générale sur la distance minimale et nous démontrons que cette estimation peut être améliorée en supposant que la surface abélienne ne contient pas de courbes absolument irréductibles de petit genre. Dans cette optique nous caractérisons toutes les surfaces abéliennes qui ne contiennent pas de courbes absolument irréductibles de genre inférieur ou égal à 2. Cette approche nous conduit naturellement à considérer les restrictions de Weil de courbes elliptiques et les surfaces abéliennes qui n'admettent pas de polarisation principale
In this thesis we provide a theoretical study of algebraic geometry codes from surfaces defined over finite fields. We prove lower bounds for the minimum distance of codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds for surfaces whose arithmetic Picard number equals one, surfaces without curves with small self-intersection and fibered surfaces. Then we apply these bounds to surfaces embedded in P3. A special attention is given to codes constructed from abelian surfaces. In this context we give a general bound on the minimum distance and we prove that this estimation can be sharpened under the assumption that the abelian surface does not contain absolutely irreducible curves of small genus. In this perspective we characterize all abelian surfaces which do not contain absolutely irreducible curves of genus up to 2. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization
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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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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 of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of Nq(g) is now known.

At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.

 

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Books on the topic "Algebraic geometric codes"

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

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Tsfasman, M. A., and S. G. Vlăduţ. Algebraic-Geometric Codes. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9.

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Barg, Alexander, and O. R. Musin. Discrete geometry and algebraic combinatorics. Providence, Rhode Island: American Mathematical Society, 2014.

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Duursma, Iwan Maynard. Decoding codes from curves and cyclic codes. [Eindhoven: Technische Universiteit Eindhoven, 1993.

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Stepanov, S. A. Codes on Algebraic Curves. Boston, MA: Springer US, 1999.

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Tsfasman, M. A. Algebraic geometry codes: Basic notions. Providence, R.I: American Mathematical Society, 2007.

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International Conference Arithmetic, Geometry, Cryptography and Coding Theory (14th 2013 Marseille, France). Algorithmic arithmetic, geometry, and coding theory: 14th International Conference, Arithmetic, Geometry, Cryptography, and Coding Theory, June 3-7 2013, CIRM, Marseille, France. Edited by Ballet Stéphane 1971 editor, Perret, M. (Marc), 1963- editor, and Zaytsev, Alexey (Alexey I.), 1976- editor. Providence, Rhode Island: American Mathematical Society, 2015.

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Blahut, Richard E. Algebraic codes on lines, planes, and curves. Cambridge: Cambridge University Press, 2008.

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Blahut, Richard E. Algebraic codes on lines, planes, and curves. Cambridge: Cambridge University Press, 2008.

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Geometry and codes. Dordrecht [Netherlands]: Kluwer Academic Publishers, 1988.

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Book chapters on the topic "Algebraic geometric codes"

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Tsfasman, M. A., and S. G. Vlăduţ. "Algebraic Curves." In Algebraic-Geometric Codes, 101–39. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_4.

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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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Tsfasman, M. A., and S. G. Vlăduţ. "Codes and Their Parameters." In Algebraic-Geometric Codes, 5–35. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_1.

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Tsfasman, M. A., and S. G. Vlăduţ. "Constructions and Properties." In Algebraic-Geometric Codes, 265–96. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_10.

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Tsfasman, M. A., and S. G. Vlăduţ. "Examples." In Algebraic-Geometric Codes, 297–329. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_11.

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Tsfasman, M. A., and S. G. Vlăduţ. "Decoding." In Algebraic-Geometric Codes, 331–47. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_12.

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Tsfasman, M. A., and S. G. Vlăduţ. "Asymptotic Results." In Algebraic-Geometric Codes, 349–85. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_13.

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Tsfasman, M. A., and S. G. Vlăduţ. "Codes on Classical Modular Curves." In Algebraic-Geometric Codes, 395–434. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_14.

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Tsfasman, M. A., and S. G. Vlăduţ. "Codes on Drinfeld Curves." In Algebraic-Geometric Codes, 435–69. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_15.

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Tsfasman, M. A., and S. G. Vlăduţ. "Polynomiality." In Algebraic-Geometric Codes, 471–510. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_16.

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Conference papers on the topic "Algebraic geometric codes"

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Hu, Wanbao. "Improved Approach to Algebraic-Geometric Codes." In 2009 International Conference on Electronic Commerce and Business Intelligence, ECBI. IEEE, 2009. http://dx.doi.org/10.1109/ecbi.2009.10.

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Ben-Aroya, Avraham, and Amnon Ta-Shma. "Constructing Small-Bias Sets from Algebraic-Geometric Codes." In 2009 IEEE 50th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2009. http://dx.doi.org/10.1109/focs.2009.44.

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Hu, Wanbao, Huaping Cai, Yanxia Wu, and Zhen Wang. "A note on relationship between algebraic geometric codes and LDPC codes." In 2010 2nd International Conference on Signal Processing Systems (ICSPS). IEEE, 2010. http://dx.doi.org/10.1109/icsps.2010.5555509.

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Shokrollahi, M. Amin, and Hal Wasserman. "Decoding algebraic-geometric codes beyond the error-correction bound." In the thirtieth annual ACM symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/276698.276753.

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Kolovanova, Ievgeniia, Anastasia Kiyan, Tetiana Kuznetsova, and Volodymir Panchenko. "Analysis and Investigation of Properties of Algebraic Geometric Codes." In 2018 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo). IEEE, 2018. http://dx.doi.org/10.1109/ukrmico43733.2018.9047556.

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Geil, Olav, Stefano Martin, Ryutaroh Matsumoto, Diego Ruano, and Yuan Luo. "Relative generalized Hamming weights of one-point algebraic geometric codes." In 2014 IEEE Information Theory Workshop (ITW). IEEE, 2014. http://dx.doi.org/10.1109/itw.2014.6970808.

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Guruswami, Venkatesan, and Anindya Patthak. "Correlated Algebraic-Geometric Codes: Improved List Decoding over Bounded Alphabets." In 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06). IEEE, 2006. http://dx.doi.org/10.1109/focs.2006.23.

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Shen, Jie, Deshan Miao, and Daoben Li. "Construction algebraic geometric LDPC codes on frequency-selective fading channels." In 2009 Global Mobile Congress. IEEE, 2009. http://dx.doi.org/10.1109/gmc.2009.5295847.

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Olshevsky, Vadim, and M. Amin Shokrollahi. "A displacement approach to efficient decoding of algebraic-geometric codes." In the thirty-first annual ACM symposium. New York, New York, USA: ACM Press, 1999. http://dx.doi.org/10.1145/301250.301311.

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Siyuan Wu, Li Chen, and Martin Johnston. "Low-complexity Chase decoding of algebraic-geometric codes using Koetter's interpolation." In 2016 IEEE Information Theory Workshop (ITW). IEEE, 2016. http://dx.doi.org/10.1109/itw.2016.7606867.

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