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
  • [21] Self-dual cyclic codes over Z4 of length 4n
    Cao, Yuan
    Cao, Yonglin
    Fu, Fang-Wei
    Wang, Guidong
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2022, 33 (01) : 21 - 51
  • [22] Generalized cyclotomic numbers and cyclic codes of prime power length over Z4
    Batra, Sudhir
    Jain, Sonal
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2019, 12 (05)
  • [23] Binary images of cyclic codes over Z4
    Wolfmann, J
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (05) : 1773 - 1779
  • [24] Cyclic codes over a linear companion of Z4
    Udaya, P
    Bonnecaze, A
    1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 398 - 398
  • [25] Reversible complement cyclic codes over Z4
    Klin-Earn, Chakkrid
    Sriwirach, Wateekorn
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2023, 15 (07)
  • [26] Cyclic codes over Z4 + uZ4
    Bandi, Rama Krishna
    Bhaintwal, Maheshanand
    2015 SEVENTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA), 2015, : 47 - 51
  • [27] Negacyclic codes over Z4 of even length
    Blackford, T
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (06) : 1417 - 1424
  • [28] Cyclic codes over Z4 + uZ4 + u2Z4
    Ozen, Mehmet
    Ozzaim, Nazmiye Tugba
    Aydin, Nuh
    TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (05) : 1235 - 1247
  • [29] Infinite families of MDR cyclic codes over Z4 via constacyclic codes over Z4[u]/⟨u2-1⟩
    Han, Nayoung
    Kim, Bohyun
    Kim, Boran
    Lee, Yoonjin
    DISCRETE MATHEMATICS, 2020, 343 (03)
  • [30] On the construction of self-dual cyclic codes over Z4 with arbitrary even length
    Cao, Yuan
    Cao, Yonglin
    Ling, San
    Wang, Guidong
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2022, 14 (05): : 1117 - 1143
12345