THE TRACE DESCRIPTION OF IRREDUCIBLE QUASI-CYCLIC CODES

被引：5
|
作者：
SEGUIN, GE
DROLET, G
机构：
[1] Department of Electrical and Computer Engineering, Royal Military College, Kingston, Ontario
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 1990年 / 36卷 / 06期
关键词：
Index Terms; irreducible quasi-cyclic codes; modules; trace function;
D O I：
10.1109/18.59946
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The notion of a q-ary irreducible quasi-cyclic code of block length n and index r is introduced. We then provide a trace description of such a code in a fashion similar to the trace description of irreducible cyclic codes. In particular, we show that an irreducible quasi-cyclic code of dimension k is completely described by an irreducible cyclic code and r elements from the field Fqk. Using this latter fact, we construct a number of binary irreducible quasi-cyclic codes of index 2 and obtain their weight spectra. © 1990 IEEE
引用
收藏
页码：1463 / 1466
页数：4
相关论文
共 50 条
  • [41] On the duals of quasi-cyclic codes and their application to quantum codes
    Benjwal, Shivanshu
    Bhaintwal, Maheshanand
    [J]. QUANTUM INFORMATION PROCESSING, 2024, 23 (04)
  • [42] New codes from chains of quasi-cyclic codes
    Grassl, M
    White, G
    [J]. 2005 IEEE International Symposium on Information Theory (ISIT), Vols 1 and 2, 2005, : 2095 - 2099
  • [43] A link between quasi-cyclic codes and convolutional codes
    Esmaeili, M
    Gulliver, TA
    Secord, NP
    Mahmoud, SA
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (01) : 431 - 435
  • [44] Linking Reversed and Dual Codes of Quasi-Cyclic Codes
    Taki Eldin, Ramy
    Matsui, Hajime
    [J]. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2022, E105A (03) : 381 - 388
  • [45] Quasi-cyclic codes as codes over rings of matrices
    Cayrel, Pierre-Louis
    Chabot, Christophe
    Necer, Abdelkader
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2010, 16 (02) : 100 - 115
  • [46] On the duals of quasi-cyclic codes and their application to quantum codes
    Shivanshu Benjwal
    Maheshanand Bhaintwal
    [J]. Quantum Information Processing, 23
  • [47] Quasi-cyclic codes as cyclic codes over a family of local rings
    Dougherty, Steven T.
    Fernandez-Cordoba, Cristina
    Ten-Valls, Roger
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2016, 40 : 138 - 149
  • [48] Good reversible quasi-cyclic codes via unfolding cyclic codes
    ElDin, Ramy Taki
    Matsui, Hajime
    [J]. IEICE COMMUNICATIONS EXPRESS, 2020, 9 (12): : 668 - 673
  • [49] On Spectral Design Methods for Quasi-Cyclic Codes
    Roth, Ron M.
    Zeh, Alexander
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (05) : 2637 - 2647
  • [50] Quasi-cyclic codes: algebraic properties and applications
    Mohamadbagher Zeraatpisheh
    Morteza Esmaeili
    T. Aaron Gulliver
    [J]. Computational and Applied Mathematics, 2020, 39
12345