메뉴 건너뛰기




Volumn 4, Issue 4, 2010, Pages 485-518

Efficient list decoding of a class of algebraic-geometry codes

Author keywords

Alekhnovich's algorithm; Algebraic geometry codes; List decoding

Indexed keywords


EID: 78649424862     PISSN: 19305346     EISSN: 19305338     Source Type: Journal    
DOI: 10.3934/amc.2010.4.485     Document Type: Article
Times cited : (23)

References (31)
  • 1
    • 78649426755 scopus 로고    scopus 로고
    • Overview of Magma v2.9 features
    • Overview of Magma v2.9 features, http://magma.maths.usyd.edu.au/magma/Features/node93.html.
  • 2
    • 23744478862 scopus 로고    scopus 로고
    • Linear Diophantine equations over polynomials and soft decoding of Reed-Solomon codes
    • M. Alekhnovich, Linear Diophantine equations over polynomials and soft decoding of Reed-Solomon codes, IEEE Transactions on Information Theory, 51 (2005), 2257-2265.
    • (2005) IEEE Transactions on Information Theory , vol.51 , pp. 2257-2265
    • Alekhnovich, M.1
  • 4
    • 0034315205 scopus 로고    scopus 로고
    • A Hensel lifting to replace factorization in list-decoding of algebraicgeometric and Reed-Solomon codes
    • D. Augot and L. Pecquet, A Hensel lifting to replace factorization in list-decoding of algebraicgeometric and Reed-Solomon codes, IEEE Transactions on Information Theory, 46 (2000), 2605-2614.
    • (2000) IEEE Transactions On Information Theory , vol.46 , pp. 2605-2614
    • Augot, D.1    Pecquet, L.2
  • 5
    • 52349089005 scopus 로고    scopus 로고
    • On the Roth and Ruckenstein equations for the Guruswami-Sudan algorithm
    • ISIT 2008
    • D. Augot and A. Zeh, On the Roth and Ruckenstein equations for the Guruswami-Sudan algorithm, in Information Theory, 2008. ISIT 2008. IEEE International Symposium, (2008), 2620-2624.
    • (2008) Information Theory. IEEE International Symposium , pp. 2620-2624
    • Augot, D.1    Zeh, A.2
  • 6
    • 77952883693 scopus 로고    scopus 로고
    • Key-equations for list decoding of Reed-Solomon codes and how to solve them
    • P. Beelen and K. Brander, Key-equations for list decoding of Reed-Solomon codes and how to solve them, Journal of Symbolic Computation, 45 (2010), 773-786.
    • (2010) Journal of Symbolic Computation , vol.45 , pp. 773-786
    • Beelen, P.1    Brander, K.2
  • 7
    • 0007371326 scopus 로고    scopus 로고
    • The Newton polygon of plane curves with many rational points
    • P. Beelen and R. Pellikaan, The Newton polygon of plane curves with many rational points, Designs, Codes and Cryptography, 21 (2000), 41-67.
    • (2000) Designs, Codes and Cryptography , vol.21 , pp. 41-67
    • Beelen, P.1    Pellikaan, R.2
  • 14
    • 0033183669 scopus 로고    scopus 로고
    • Improved decoding of Reed-Solomon and algebraic-geometric codes
    • V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometric codes, IEEE Transactions On Information Theory, 45 (1999), 1757-1767.
    • (1999) IEEE Transactions on Information Theory , vol.45 , pp. 1757-1767
    • Guruswami, V.1    Sudan, M.2
  • 15
    • 84957649180 scopus 로고    scopus 로고
    • Decoding Hermitian codes with Sudan's algorithm
    • eds. M. Fossorier, H. Imai, S. Lin and A. Poli), Springer-Verlag
    • T. Høholdt and R. R. Nielsen, Decoding Hermitian codes with Sudan's algorithm, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (eds. M. Fossorier, H. Imai, S. Lin and A. Poli), Springer-Verlag, (1999), 260-270.
    • (1999) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes , pp. 260-270
    • Høholdt, T.1    Nielsen, R.R.2
  • 17
  • 18
    • 42649130660 scopus 로고    scopus 로고
    • List decoding of Reed-Solomon codes from a Gr̈obner basis perspective
    • K. Lee and M. E. O'Sullivan, List decoding of Reed-Solomon codes from a Gr̈obner basis perspective, Journal of Symbolic Computation, 43 (2008), 645-658.
    • (2008) Journal of Symbolic Computation , vol.43 , pp. 645-658
    • Lee, K.1    O'Sullivan, M.E.2
  • 19
    • 0038370159 scopus 로고
    • Geometric-Goppa codes on some maximal curves and their minimum distance
    • Shizuoka, Japan
    • S. Miura and N. Kamiya, Geometric-Goppa codes on some maximal curves and their minimum distance, in Proceedings of 1993 IEEE Information Theory Workshop, Shizuoka, Japan, (1993), 85-86.
    • (1993) Proceedings of 1993 IEEE Information Theory Workshop , pp. 85-86
    • Miura, S.1    Kamiya, N.2
  • 20
  • 21
    • 34848871321 scopus 로고    scopus 로고
    • Gr̈obner basis approach to list decoding of algebraic geometry codes, Applicable Algebra in Engineering
    • H. O'Keeffe and P. Fitzpatrick, Gr̈obner basis approach to list decoding of algebraic geometry codes, Applicable Algebra in Engineering, Communication and Computing, 18 (2007), 445-466.
    • (2007) Communication and Computing , vol.18 , pp. 445-466
    • O'Keeffe, H.1    Fitzpatrick, P.2
  • 23
    • 78649413048 scopus 로고    scopus 로고
    • V. S. Pless and W. C. Huffman (eds.), North-Holland
    • V. S. Pless and W. C. Huffman (eds.), Handbook of Coding Theory, North-Holland, 1 (1998).
    • (1998) Handbook of Coding Theory , vol.1
  • 25
    • 69849091619 scopus 로고    scopus 로고
    • On fast interpolation method for Guruswami-Sudan list decoding of one-point algebraic-geometry codes
    • AAECC
    • S. Sakata, On fast interpolation method for Guruswami-Sudan list decoding of one-point algebraic-geometry codes, in AAECC, (2001), 172-181.
    • (2001) , pp. 172-181
    • Sakata, S.1
  • 26
    • 84892316200 scopus 로고    scopus 로고
    • M. Sala, T. Mora, L. Perret, S. Sakata and C. Traverso (eds.), Springer
    • M. Sala, T. Mora, L. Perret, S. Sakata and C. Traverso (eds.), Gr̈obner Bases, Coding, and Cryptography, Springer, 2009.
    • (2009) Gr̈obner Bases, Coding, and Cryptography
  • 30
    • 0031097176 scopus 로고    scopus 로고
    • Decoding of Reed-Solomon codes beyond the error-correction bound
    • M. Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound, Journal of Complexity, 13 (1997), 180-193.
    • (1997) Journal of Complexity , vol.13 , pp. 180-193
    • Sudan, M.1
  • 31
    • 0035441838 scopus 로고    scopus 로고
    • Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes
    • X.-W. Wu and P. H. Siegel, Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes, IEEE Transactions On Information Theory, 47 (2001), 2579-2587.
    • (2001) IEEE Transactions on Information Theory , vol.47 , pp. 2579-2587
    • Wu, X.-W.1    Siegel, P.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.