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
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 24卷
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
  • [1] On quasi-cyclic codes
    Heijnen, P
    van Tilborg, H
    Weijs, S
    1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 65 - 65
  • [2] Quasi-cyclic codes with cyclic constituent codes
    Lim, Chong Jie
    FINITE FIELDS AND THEIR APPLICATIONS, 2007, 13 (03) : 516 - 534
  • [3] On quasi-cyclic codes as a generalization of cyclic codes
    Barbier, M.
    Chabot, C.
    Quintin, G.
    FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (05) : 904 - 919
  • [4] Quasi-cyclic and generalized quasi-cyclic codes and uniqueness of their generators
    Abualrub, Taher
    Seneviratne, Padmapani
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2023, 15 (06)
  • [5] QUASI-CYCLIC SUBCODES OF CYCLIC CODES
    Belfiore, Jean-Claude
    Guneri, Cem
    Ozkaya, Buket
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2017, 31 (02) : 1454 - 1475
  • [6] A NOTE ON QUASI-CYCLIC CODES
    DASS, BK
    WASAN, SK
    INTERNATIONAL JOURNAL OF ELECTRONICS, 1983, 54 (01) : 91 - 94
  • [7] Lattices of quasi-cyclic codes
    Bracco, AD
    EUROPEAN JOURNAL OF COMBINATORICS, 2004, 25 (04) : 505 - 516
  • [8] Quaternary quasi-cyclic codes
    Pei Jun-ying
    Zhang Xue-jun
    APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2008, 23 (03) : 359 - 365
  • [9] Notes on Quasi-Cyclic Codes with Cyclic Constituent Codes
    Shi, Minjia
    Zhang, Yiping
    Sole, Patrick
    MATHEMATICS ACROSS CONTEMPORARY SCIENCES, 2017, 190 : 193 - 206
  • [10] On quintic quasi-cyclic codes
    Bracco, Anne Desideri
    Natividad, Ann Marie
    Sole, Patrick
    DISCRETE APPLIED MATHEMATICS, 2008, 156 (18) : 3362 - 3375
12345