Quasi-cyclic NMDS codes

被引:3
|
作者
Tong, Hongxi [1 ]
Yang, Ding [1 ]
机构
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
基金
中国国家自然科学基金;
关键词
Cyclic codes; Quasi-cyclic codes; NMDS codes; Elliptic curves; Elliptic function fields; Algebraic geometry codes; NEAR-MDS CODES; ALGEBRAIC STRUCTURE; FIELDS;
D O I
10.1016/j.ffa.2013.05.008
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Quasi-cyclic (QC) codes constitute a remarkable generalization of cyclic codes, and near-MDS (NMDS) codes are a family of codes obtained by weakening the restrictions of MDS codes. In this paper, we consider the QC NMDS codes by combining these two concepts. By choosing some elliptic curves with many rational points, we give a construction of QC NMDS codes based on the action of an elliptic curve automorphism on the rational points of the curve. Moreover, we calculate explicit example over finite fields of characteristic 2, 3, 5 or 7. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:45 / 54
页数:10
相关论文
共 50 条
  • [31] Quantum quasi-cyclic LDPC codes
    Hagiwara, Manabu
    Imai, Hideki
    2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7, 2007, : 806 - +
  • [32] Quasi-cyclic Goppa codes.
    Berger, TP
    2000 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2000, : 195 - 195
  • [33] LONG QUASI-CYCLIC CODES ARE GOOD
    WELDON, EJ
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1970, 16 (01) : 130 - +
  • [34] Binary quasi-cyclic Goppa codes
    Bommier, G
    Blanchet, F
    DESIGNS CODES AND CRYPTOGRAPHY, 2000, 20 (02) : 107 - 124
  • [35] 1-Generator quasi-cyclic and generalized quasi-cyclic codes over the ring
    Gao, Yun
    Gao, Jian
    Wu, Tingting
    Fu, Fang-Wei
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2017, 28 (06) : 457 - 467
  • [36] New quasi-cyclic codes from simplex codes
    Chen, Eric Z.
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (03) : 1193 - 1196
  • [37] On the duals of quasi-cyclic codes and their application to quantum codes
    Benjwal, Shivanshu
    Bhaintwal, Maheshanand
    QUANTUM INFORMATION PROCESSING, 2024, 23 (04)
  • [38] New codes from chains of quasi-cyclic codes
    Grassl, M
    White, G
    2005 IEEE International Symposium on Information Theory (ISIT), Vols 1 and 2, 2005, : 2095 - 2099
  • [39] Linking Reversed and Dual Codes of Quasi-Cyclic Codes
    Taki Eldin, Ramy
    Matsui, Hajime
    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2022, E105A (03) : 381 - 388
  • [40] A link between quasi-cyclic codes and convolutional codes
    Esmaeili, M
    Gulliver, TA
    Secord, NP
    Mahmoud, SA
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (01) : 431 - 435