Les codes algébriques principaux et leur décodage
Les cours du CIRM (2010)
- Volume: 1, Issue: 2, page 31-74
- ISSN: 2108-7164
Access Full Article
topHow to cite
topAugot, Daniel. "Les codes algébriques principaux et leur décodage." Les cours du CIRM 1.2 (2010): 31-74. <http://eudml.org/doc/116370>.
@article{Augot2010,
author = {Augot, Daniel},
journal = {Les cours du CIRM},
language = {fre},
number = {2},
pages = {31-74},
publisher = {CIRM},
title = {Les codes algébriques principaux et leur décodage},
url = {http://eudml.org/doc/116370},
volume = {1},
year = {2010},
}
TY - JOUR
AU - Augot, Daniel
TI - Les codes algébriques principaux et leur décodage
JO - Les cours du CIRM
PY - 2010
PB - CIRM
VL - 1
IS - 2
SP - 31
EP - 74
LA - fre
UR - http://eudml.org/doc/116370
ER -
References
top- J. B. Ashbrook, N. R. Shanbhag, R. Koetter, R. E. Blahut, Implementation of a Hermitian decoder IC in 0.35 m CMOS, Custom Integrated Circuits, 2001, IEEE Conference on. (2001), 297-300
- E.F. Assmus, J.D. Key, Polynomial codes and finite geometries, Handbook of coding theory II (1998), PlessV.S.V. Zbl0980.94038MR1667952
- Elwyn R. Berlekamp, Algebraic coding theory, (1968), McGraw-Hill Zbl0988.94521MR238597
- Elwyn R. Berlekamp, Robert J. McEliece, Henk C. A. van Tilborg, On the inherent intractability of certain coding problems, IEEE Transactions on Information Theory 24 (1978), 384-386 Zbl0377.94018MR495180
- Richard E. Blahut, Fast Algorithms for Digital Signal Processing, (1985), Addison-Wesley Zbl0579.94001MR777867
- Richard E. Blahut, Algebraic Codes for Data Transmission, (2002), Cambridge University Press Zbl1204.94002
- J. Bruck, M. Naor, The hardness of decoding linear codes with preprocessing, IEEE Transactions on Information Theory 36 (1990), 381-385 Zbl0704.94022MR1052788
- Qi Cheng, Hard Problems of Algebraic Geometry Codes, (2005) Zbl1308.94113
- Qi Cheng, Daqing Wan, Complexity of Decoding Positive-Rate Reed-Solomon Codes, ICALP ’08 : Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I (2008), 283-293, Springer-Verlag, Berlin, Heidelberg Zbl1153.94468MR2500279
- Chien-Yu Chien, I. M. Duursma, Geometric Reed-Solomon codes of length 64 and 65 over , Information Theory, IEEE Transactions on 49 (2003), 1351-1353 Zbl1063.94107MR1984834
- R. T. Chien, Cyclic decoding procedures for Bose-Chaudhuri-Hocquenghem codes, IEEE Transactions on Information Theory 10 (1964), 357-363 Zbl0125.09503
- David Cox, John Littel, Donal O’Shea, Ideals, Varieties and Algorithms, (1992), Springer MR1189133
- G. L. Feng, T. R. N. Rao, Decoding algebraic-geometric codes up to the designed minimum distance, Information Theory, IEEE Transactions on 39 (1993), 37-45 Zbl0765.94021MR1211489
- Gui-Liang Feng, Kenneth K. Tzeng, A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes, IEEE Transactions on Information Theory 37 (1991), 1274-1287 Zbl0734.94008MR1136665
- G. Forney, On decoding BCH codes, Information Theory, IEEE Transactions on 11 (1965), 549-557 Zbl0143.41401MR189923
- Philippe Gaborit, Gilles Zemor, Asymptotic improvement of the Gilbert-Varshamov bound for binary linear codes, Information Theory, 2006 IEEE International Symposium on (2006), 287-291 Zbl1318.94120
- Peter Gemmell, Madhu Sudan, Highly resilient correctors for polynomials, Information Processing Letters 43 (1992), 169-174 Zbl0767.68075MR1187182
- V. D. Goppa, Codes that are associated with divisors, Problemy Pereda ci Informacii 13 (1977), 33-39 Zbl0415.94005MR497293
- V. Guruswami, M. Sudan, On representations of algebraic-geometry codes, Information Theory, IEEE Transactions on 47 (2001), 1610-1613 Zbl1002.94041MR1830110
- V. Guruswami, A. Vardy, Maximum-likelihood decoding of Reed-Solomon codes is NP-hard, Information Theory, IEEE Transactions on 51 (2005), 2249-2256 Zbl1310.94210MR2246360
- Venkatesan Guruswami, Algorithmic results in list decoding, (2007), Now Publishers Inc Zbl1203.94139MR2453147
- Venkatesan Guruswami, List Decoding of Binary Codes - A Brief Survey of Some Recent Results, Coding and Cryptology 5557 (2009), 97-106, Springer Berlin Heidelberg, Berlin, Heidelberg Zbl1248.94123
- Venkatesan Guruswami, Anindya C. Patthak, Correlated algebraic-geometric codes : Improved list decoding over bounded alphabets, Mathematics of computation (2007) Zbl1150.94013MR2353961
- Venkatesan Guruswami, Atri Rudra, Explicit capacity-achieving list-decodable codes, STOC ’06 : Proceedings of the thirty-eighth annual ACM symposium on Theory of computing (2006), 1-10, ACM, New York, NY, USA Zbl1301.94157MR2277125
- Venkatesen Guruswami, Madhu Sudan, Extensions to the Johnson bound, (2001)
- R. W. Hamming, Error detecting and error correcting codes, (1950) MR35935
- Tom Høholdt, Ruud Pellikaan, On the decoding of algebraic-geometric codes, IEEE Transactions on Information Theory 41 (1995), 1589-1614 Zbl0847.94012MR1391018
- T. Høholdt, J. H. van Lint, R. Pellikaan, Handbook of Coding Theory, I (1998), 871-961, Elsevier Zbl0922.94015
- Jørn Justesen, Tom Høholdt, Bounds on list decoding of MDS codes, IEEE Transactions on Information Theory 47 (2001), 1604-1609 Zbl0997.94030MR1830109
- R. Kotter, A fast parallel implementation of a Berlekamp-Massey algorithm for algebraic-geometric codes, IEEE Transactions on Information Theory 44 (1998), 1353-1368 Zbl0994.94037MR1665770
- F. J. Macwilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes, (1983), North Holland Zbl0657.94010
- Jim Massey, Shift-register synthesis and BCH decoding, IEEE Transactions on Information Theory 15 (1969), 122-127 Zbl0167.18101MR242556
- Hajime Matsui, Shojiro Sakata, Masazumi Kurihara, Seiichi Mita, Systolic array architecture implementing Berlekamp-Massey-Sakata algorithm for decoding codes on a class of algebraic curves, IEEE Transactions on Information Theory 51 (2005), 3856-3871 Zbl1317.94158MR2239003
- Robert J. McEliece, The Guruswami-Sudan Decoding Algorithm for Reed-Solomon Codes, (2003)
- K. Saints, C. Heegard, Algebraic-geometric codes and multidimensional cyclic codes : a unified theory and algorithms for decoding using Grobner bases, Information Theory, IEEE Transactions on 41 (1995), 1733-1751 Zbl0861.94031MR1391032
- S. Sakata, J. Justesen, Y. Madelung, H. E. Jensen, T. Hoholdt, Fast decoding of algebraic-geometric codes up to the designed minimum distance, Information Theory, IEEE Transactions on 41 (1995), 1672-1677 Zbl0847.94013MR1391026
- Shojiro Sakata, Finding a Minimal Set of Linear Recurring Relations Capable of Generating a Given Finite Two-Dimensional Array, J. Symb. Comput. 5 (1988), 321-337 Zbl0647.68044MR946587
- Shojiro Sakata, N-Dimensional Berlekamp-Massey Algorithm for Multiple Arrays and Construction of Multivariate Polynomials with Preassigned Zeros, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes 6th International Conference, AAECC-6 Rome 357 (1988), 356-376, MoraTeoT. Zbl0675.13012MR1008512
- Shojiro Sakata, Finding a minimal polynomial vector set of a vector of nD arrays, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (1991), 414-425, Springer-Verlag Zbl0782.94007MR1229338
- Eli B. Sasson, Swastik Kopparty, Jaikumar Radhakrishnan, Subspace Polynomials and List Decoding of Reed-Solomon Codes, FOCS ’06 : Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (2006), 207-216, IEEE Computer Society, Washington, DC, USA
- J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities, Journal of the ACM 27 (1980), 701-717 Zbl0452.68050MR594695
- Claude E. Shannon, A mathematical theory of Communication, The Bell system technical journal 27 (1948), 379-423 Zbl1154.94303MR26286
- Mohammad A. Shokrollahi, Hal Wasserman, Decoding algebraic geometric codes, Proceedings of the IEEE Information Theory Workshop, 1998 (1998), 40-41 Zbl1027.68605
- Henning Stichtenoth, Algebraic Function Fields and Codes, (1993), Springer Zbl0816.14011MR1251961
- Madhu Sudan, Decoding of Reed-Solomon Codes beyond the Error-Correction Bound, Journal of Complexity 13 (1997), 180-193 Zbl0872.68026MR1449766
- Michael A. Tsfasman, Serguei G. Vlǎduţ, Th. Zink, Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound, Math. Nachr. 109 (1982), 21-28 Zbl0574.94013MR705893
- Alexander Vardy, Algorithmic complexity in coding theory and the minimum distance problem, STOC ’97 : Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, El Paso, United States (1997), 92-109, ACM Press Zbl0962.68060MR1715628
- Joachim von zur Gathen, Jürgen Gerhard, Modern Computer Algebra, (1999), Cambridge University Press Zbl0936.11069MR1689167
- B. E. Wahlen, J. Jimenez, Performance comparison of Hermitian and Reed-Solomon codes, MILCOM 97 Proceedings 1 (1997), 15-19 vol.1
- Loyd R. Welch, Elwyn R. Berlekamp, Error correction for algebraic block codes, US Patent 4 633 470 (1986)
- Y. Wu, New List Decoding Algorithms for Reed-Solomon and BCH Codes, Information Theory, IEEE Transactions on 54 (2008), 3611-3630 Zbl1329.94103MR2451017
- Richard Zippel, Probabilistic algorithms for sparse polynomials, Symbolic and Algebraic Computation : EUROSAM ’79 72 (1979), 216-226, Springer Zbl0418.68040MR575692
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.