On quasi-cyclic codes as a generalization of cyclic codes

被引：20
|
作者：
Barbier, M. [1 ]
Chabot, C. [2 ]
Quintin, G. [1 ]
机构：
[1] Ecole Polytech, Lab Informat LIX, F-91128 Palaiseau, France
[2] LJK, F-38041 Grenoble 09, France
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2012年 / 18卷 / 05期
关键词：
Quasi-cyclic codes; Left ideals; Matrix rings; Cyclic codes; Evaluation codes; Key equation; ALGEBRAIC STRUCTURE; MCELIECE;
D O I：
10.1016/j.ffa.2012.06.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic codes. We show a one-to-one correspondence between l-quasi-cyclic codes of length me and left ideals of M-l(F-q)[x]/(X-m - 1). Then, we generalize BCH codes and evaluation codes in this context. We study their parameters and establish a key equation. Finally. we present a new [189, 11, 125]F-4 code beating the known minimum distance for fixed length and dimension. Many codes with good parameters beating best known ones have been found from this latter. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：904 / 919
页数：16
相关论文
共 50 条
  • [1] Quasi-cyclic codes with cyclic constituent codes
    Lim, Chong Jie
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2007, 13 (03) : 516 - 534
  • [2] On quasi-cyclic codes
    Heijnen, P
    van Tilborg, H
    Weijs, S
    [J]. 1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 65 - 65
  • [3] Notes on Quasi-Cyclic Codes with Cyclic Constituent Codes
    Shi, Minjia
    Zhang, Yiping
    Sole, Patrick
    [J]. MATHEMATICS ACROSS CONTEMPORARY SCIENCES, 2017, 190 : 193 - 206
  • [4] QUASI-CYCLIC SUBCODES OF CYCLIC CODES
    Belfiore, Jean-Claude
    Guneri, Cem
    Ozkaya, Buket
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2017, 31 (02) : 1454 - 1475
  • [5] Quasi-Cyclic Codes Via Unfolded Cyclic Codes and Their Reversibility
    Eldin, Ramy Taki
    Matsui, Hajime
    [J]. IEEE ACCESS, 2019, 7 : 184500 - 184508
  • [6] Quasi-cyclic and generalized quasi-cyclic codes and uniqueness of their generators
    Abualrub, Taher
    Seneviratne, Padmapani
    [J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2023, 15 (06)
  • [7] Quaternary quasi-cyclic codes
    Pei Jun-ying
    Zhang Xue-jun
    [J]. APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2008, 23 (03) : 359 - 365
  • [8] Quasi-cyclic NMDS codes
    Tong, Hongxi
    Yang, Ding
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2013, 24 : 45 - 54
  • [9] On quintic quasi-cyclic codes
    Bracco, Anne Desideri
    Natividad, Ann Marie
    Sole, Patrick
    [J]. DISCRETE APPLIED MATHEMATICS, 2008, 156 (18) : 3362 - 3375
  • [10] A NOTE ON QUASI-CYCLIC CODES
    DASS, BK
    WASAN, SK
    [J]. INTERNATIONAL JOURNAL OF ELECTRONICS, 1983, 54 (01) : 91 - 94
12345