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 11 条
  • [1] 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
  • [2] ABUALRUB T, 2003, DISCR APPL MATH, V3
  • [3] Type II codes over Z(4)
    Bonnecaze, A
    Sole, P
    Bachoc, C
    Mourrain, B
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1997, 43 (03) : 969 - 976
  • [4] Type IV self-dual codes over rings
    Dougherty, ST
    Gaborit, P
    Harada, M
    Munemasa, A
    Solé, P
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (07) : 2345 - 2360
  • [5] Maximum distance codes over rings of order 4
    Dougherty, ST
    Shiromoto, K
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (01) : 400 - 404
  • [6] On the design of space-time and space-frequfency codes for MIMO frequency-selective fading channels
    El Gamal, H
    Hammons, AR
    Liu, YJ
    Fitz, MP
    Takeshita, OY
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (09) : 2277 - 2292
  • [7] THE Z4-LINEARITY OF KERDOCK, PREPARATA, GOETHALS, AND RELATED CODES
    HAMMONS, AR
    KUMAR, PV
    CALDERBANK, AR
    SLOANE, NJA
    SOLE, P
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1994, 40 (02) : 301 - 319
  • [8] A rank criterion for QAM space-time codes
    Liu, YJ
    Fitz, MP
    Takeshita, OY
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (12) : 3062 - 3079
  • [9] Mac Williams F., 1977, THEORY ERROR CORRECT
  • [10] Pless V., 1998, INTRO THEORY ERROR C, Vthird
12