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

页码：291 / 309

页数：19

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