AN EXPLICIT REPRESENTATION AND ENUMERATION FOR NEGACYCLIC CODES OF LENGTH 2kn OVER Z4 + uZ4

被引：6
|
作者：
Cao, Yuan [1 ,2 ,3 ]
Cao, Yonglin [1 ]
Dinh, Hai Q. [4 ,5 ]
Bandi, Ramakrishna [6 ]
Fu, Fang-Wei [7 ,8 ]
机构：
[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Shandong, Peoples R China
[2] Hubei Univ, Key Lab Appl Math, Fac Math & Stat, Wuhan 430062, Peoples R China
[3] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China
[4] Ton Duc Thang Univ, Div Computat Math & Engn, Inst Computat Sci, Ho Chi Minh City, Vietnam
[5] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam
[6] Dr SPM IIIT Naya Raipur, Dept Math, Atal Nagar 493661, India
[7] Nankai Univ, Tianjin Key Lab Network & Data Secur Technol, Chern Inst Math, Tianjin 300071, Peoples R China
[8] Nankai Univ, Tianjin Key Lab Network & Data Secur Technol, LPMC, Tianjin 300071, Peoples R China
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2021年 / 15卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Negacyclic codes; Mass formula; Galois rings; finite chain rings; CYCLIC CODES; CONSTACYCLIC CODES; CONCATENATED STRUCTURE; RINGS;
D O I：
10.3934/amc.2020067
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we give an explicit representation and enumeration for negacyclic codes of length 2(k)n over the local non-principal ideal ring R = Z(4) + uZ(4) (u(2) = 0), where k, n are arbitrary positive integers and n is odd. In particular, we present all distinct negacyclic codes of length 2(k) over R precisely. Moreover, we provide an exact mass formula for the number of negacyclic codes of length 2(k)n over R and correct several mistakes in some literatures.
引用
收藏
页码：291 / 309
页数：19
相关论文
共 50 条
  • [1] A mass formula for negacyclic codes of length 2k and some good negacyclic codes over Z4 + uZ4
    Bandi, Rama Krishna
    Bhaintwal, Maheshanand
    Aydin, Nuh
    [J]. CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2017, 9 (02): : 241 - 272
  • [2] Cyclic codes over Z4 + uZ4
    Bandi, Rama Krishna
    Bhaintwal, Maheshanand
    [J]. 2015 SEVENTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA), 2015, : 47 - 51
  • [3] DUADIC CODES OVER Z4 + uZ4
    Kumar, Raj
    Bhaintwal, Maheshanand
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2020, : 404 - 417
  • [4] Cyclic codes over Z4 + uZ4 + u2Z4
    Ozen, Mehmet
    Ozzaim, Nazmiye Tugba
    Aydin, Nuh
    [J]. TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (05) : 1235 - 1247
  • [5] *Self-Dual Cyclic Codes over Z4 + uZ4
    Luo, Rong
    Parampalli, Udaya
    [J]. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2017, E100A (04) : 969 - 974
  • [6] (1+u)-Constacyclic codes over Z4 + uZ4
    Yu, Haifeng
    Wang, Yu
    Shi, Minjia
    [J]. SPRINGERPLUS, 2016, 5
  • [7] Self-dual Cyclic Codes Over Z4 + uZ4
    Luo, Rong
    Parampalli, Udaya
    [J]. 2015 SEVENTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA), 2015, : 65 - 69
  • [8] Skew cyclic codes over Z4 + uZ4 + vZ4
    Caliskan, Basri
    Aydin, Nuh
    Liu, Peihan
    [J]. CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2023, 15 (04): : 845 - 858
  • [9] Negacyclic codes over Z4 of even length
    Blackford, T
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (06) : 1417 - 1424
  • [10] Negacyclic codes of length 2(k) over Z4+uZ(4)
    Bandi, Rama Krishna
    Bhaintwal, Maheshanand
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2017, 94 (03) : 454 - 470
12345