A mass formula and rank of Z4 cyclic codes of length 2e

被引：27
|
作者：
Abualrub, T [1 ]
Ghrayeb, A
Oehmke, RH
机构：
[1] Amer Univ Sharjah, Dept Math & Stat, Sharjah, U Arab Emirates
[2] Concordia Univ, Dept Elect & Comp Engn, Montreal, PQ H3G 1M8, Canada
[3] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2004年 / 50卷 / 12期
基金：
加拿大自然科学与工程研究理事会;
关键词：
cyclic codes; dual codes; self-dual codes;
D O I：
10.1109/TIT.2004.838109
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this correspondence, we study cyclic codes of length n = 2(e) over the ring R-4 = Z(4) [x]/(x(n) - 1). In particular, we derive a closed-form expression for the number of these codes for a given length n. We also study the rank of these codes and derive an expression for that. Furthermore, we give an example in which we study all cyclic codes of length 8. We also study all self-dual codes of length 8 and 16 and classify them according to their type.
引用
收藏
页码：3306 / 3312
页数：7
相关论文
共 50 条
  • [31] On generalized quasi-cyclic codes over Z4
    Meng, Xiangrui
    Gao, Jian
    Fu, Fang-Wei
    DISCRETE MATHEMATICS, 2024, 347 (03)
  • [32] Z2Z4-Additive Cyclic Codes: Kernel and Rank
    Borges, Joaquim
    Dougherty, Steven T.
    Fernandez-Cordoba, Cristina
    Ten-Valls, Roger
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (04) : 2119 - 2127
  • [33] On the optimal Z4 codes of type II and length 16
    Duursma, IM
    Greferath, M
    Schmidt, SE
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2000, 92 (01) : 77 - 82
  • [34] Some Results on Triple Cyclic Codes over Z4
    Wu, Tingting
    Gao, Jian
    Fu, Fang-Wei
    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2016, E99A (05) : 998 - 1004
  • [35] Cyclic codes of length 2e Over F2+uF2
    Li, Ping
    Zhu, Shi-Xin
    Dianzi Yu Xinxi Xuebao/Journal of Electronics and Information Technology, 2007, 29 (05): : 1124 - 1126
  • [36] CYCLIC AND CONSTACYCLIC CODES OVER Z4 + wZ4
    Aydin, Nuh
    Cengellenmis, Yasemin
    Dertli, Abdullah
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2024, 61 (06) : 1447 - 1457
  • [37] CYCLIC CODES OF LENGTH 2(n) OVER Z(4)
    Woo, Sung Sik
    COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2013, 28 (01): : 39 - 54
  • [38] Codes over Z4
    Helleseth, T
    COMPUTATIONAL DISCRETE MATHEMATICS: ADVANCED LECTURES, 2001, 2122 : 47 - 55
  • [39] Construction and enumeration for self-dual cyclic codes over Z4 of oddly even length
    Cao, Yuan
    Cao, Yonglin
    Dougherty, Steven T.
    Ling, San
    DESIGNS CODES AND CRYPTOGRAPHY, 2019, 87 (10) : 2419 - 2446
  • [40] Maximum distance separable codes over Z4 and Z2 x Z4
    Bilal, M.
    Borges, J.
    Dougherty, S. T.
    Fernandez-Cordoba, C.
    DESIGNS CODES AND CRYPTOGRAPHY, 2011, 61 (01) : 31 - 40
12345