Cyclic codes of length 2e over Z4

被引：15
|
作者：
Abualrub, T
Oehmke, R
机构：
[1] American Univ Sharjah, Sharjah, U Arab Emirates
[2] Univ Iowa, Iowa City, IA USA
来源：
DISCRETE APPLIED MATHEMATICS | 2003年 / 128卷 / 01期
关键词：
cyclic codes; linear codes; rings; ideals;
D O I：
10.1016/S0166-218X(02)00432-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Cyclic codes of odd length over Z(4) have been studied by many authors. But what is the form of cylic codes of even length? The structure of cyclic codes of length n = 2(e), for any positive integer a is considered. We show that any cyclic code is an ideal in the ring R-n = Z(4)[x]/<x(n)-1>. We show that the ring R-n is a local ring but not a principal ideal ring. Also, we find the set of generators for cyclic codes. Examples of cyclic codes of such length are given. (C) 2003 Published by Elsevier Science B.V.
引用
收藏
页码：3 / 9
页数：7
相关论文
共 50 条
  • [1] On the distances of cyclic codes of length 2e over Z4
    Kai, Xiaoshan
    Zhu, Shixin
    [J]. DISCRETE MATHEMATICS, 2010, 310 (01) : 12 - 20
  • [2] On the generators of Z4 cyclic codes of length 2e
    Abualrub, T
    Oehmke, R
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (09) : 2126 - 2133
  • [3] The rank of Z4 cyclic codes of length 2e
    Abualrub, T
    Ghrayeb, A
    Oehmke, RH
    [J]. ISCCSP : 2004 FIRST INTERNATIONAL SYMPOSIUM ON CONTROL, COMMUNICATIONS AND SIGNAL PROCESSING, 2004, : 651 - 654
  • [4] A mass formula for Z4 cyclic codes of length 2e
    Abualrub, T
    Ghrayeb, A
    Oehmke, RH
    [J]. 2004 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2004, : 488 - 488
  • [5] A mass formula and rank of Z4 cyclic codes of length 2e
    Abualrub, T
    Ghrayeb, A
    Oehmke, RH
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (12) : 3306 - 3312
  • [6] On the Depth Distribution of Constacyclic Codes over Z4 of Length 2e
    ZHU Shixin
    HUANG Shan
    LI Jin
    [J]. Chinese Journal of Electronics, 2019, 28 (03) : 462 - 469
  • [7] On the Depth Distribution of Constacyclic Codes over Z4 of Length 2e
    Zhu Shixin
    Huang Shan
    Li Jin
    [J]. CHINESE JOURNAL OF ELECTRONICS, 2019, 28 (03) : 462 - 469
  • [8] Cyclic codes over Z4 of even length
    Dougherty, ST
    Ling, S
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2006, 39 (02) : 127 - 153
  • [9] Cyclic codes of even length over Z4
    Woo, Sung Sik
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2007, 44 (03) : 697 - 706
  • [10] On the generators of Z4 cyclic codes of length 2e (vol 49, pg 2126, 2003)
    Abualrub, T
    Oehmke, R
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (08) : 3009 - 3009
12345