Decoding Reed-Solomon Skew-Differential Codes

被引：1
作者：
Gomez-Torrecillas, Jose [1 ,2 ]
Navarro, Gabriel [3 ,4 ]
Patricio Sanchez-Hernandez, Jose [2 ]
机构：
[1] Univ Granada, IMAG, Granada 18071, Spain
[2] Univ Granada, Dept Algebra, Granada 18071, Spain
[3] Univ Granada, CITIC, Granada 18071, Spain
[4] Univ Granada, Dept Comp Sci & Artificial Intelligence, Granada 18071, Spain
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2021年 / 67卷 / 12期
关键词：
Codes; Decoding; Reed-Solomon codes; Additives; Kernel; Convolutional codes; Linear codes; convolutional codes; decoding; skew codes; CONVOLUTIONAL-CODES; ALGORITHM; RANK;
D O I：
10.1109/TIT.2021.3117083
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, the first part of the paper develops a direct presentation of the codes by means of parity-check matrices, and the decoding algorithm rests upon matrix and linear maps manipulations. The somewhat more sophisticated mathematical context (non-commutative rings) needed for the proof of the correctness of the decoding algorithm is postponed to the second part. A final section locates the Reed-Solomon skew-differential codes introduced here within the general context of codes defined by means of skew polynomial rings.
引用
收藏
页码：7891 / 7903
页数：13
相关论文
共 34 条
  • [1] Erasure coding for distributed storage: an overview
    Balaji, S. B.
    Krishnan, M. Nikhil
    Vajha, Myna
    Ramkumar, Vinayak
    Sasidharan, Birenjith
    Kumar, P. Vijay
    [J]. SCIENCE CHINA-INFORMATION SCIENCES, 2018, 61 (10)
  • [2] Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric
    Bartz, Hannes
    Jerkovits, Thomas
    Puchinger, Sven
    Rosenkilde, Johan
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2021, 67 (08) : 5026 - 5050
  • [3] Skew-cyclic codes
    Boucher, D.
    Geiselmann, W.
    Ulmer, F.
    [J]. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2007, 18 (04) : 379 - 389
  • [4] Linear codes using skew polynomials with automorphisms and derivations
    Boucher, D.
    Ulmer, F.
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2014, 70 (03) : 405 - 431
  • [5] An algorithm for decoding skew Reed-Solomon codes with respect to the skew metric
    Boucher, Delphine
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2020, 88 (09) : 1991 - 2005
  • [6] Coding with skew polynomial rings
    Boucher, Delphine
    Ulmer, Felix
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2009, 44 (12) : 1644 - 1656
  • [7] Bueso J., 2003, Algorithmic Methods in Non-Commutative Algebra
  • [8] Caruso X., 2019, ARXIV190808430
  • [9] Noncommutative symmetric functions and W-polynomials
    Delenclos, Jonathan
    Leroy, Andre
    [J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2007, 6 (05) : 815 - 837
  • [10] CONVOLUTIONAL CODES .1. ALGEBRAIC STRUCTURE
    FORNEY, GD
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1970, 16 (06) : 720 - +
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