Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings

被引：0

作者：

Dinh, Hai Q. ^{[1
]}

Liu, Hualu ^{[2
]}

Tansuchat, Roengchai ^{[3
]}

Vo, Thang M. ^{[4
,5
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Hubei Univ Technol, Sch Sci, Wuhan 430068, Peoples R China

[3] Chiang Mai Univ, Fac Econ, Ctr Excellence Econometr, Chiang Mai 52000, Thailand

[4] Ohio Univ, Dept Math, Athens, OH 45701 USA

[5] Ind Univ Vinh, Dept Gen Educ, Vinh City, Vietnam

来源：

ALGEBRA COLLOQUIUM | 2021年 / 28卷 / 04期

关键词：

negacyclic codes; repeated-root codes; symbol-pair distance; MDS codes; CYCLIC CODES; CONSTACYCLIC CODES; EXPLICIT REPRESENTATION; HAMMING DISTANCES; Z(4); ENUMERATION; PREPARATA; KERDOCK;

D O I：

10.1142/S1005386721000468

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Negacyclic codes of length 2(s) over the Galois ring GR(2(a), m) are linearly ordered under set-theoretic inclusion, i.e., they are the ideals <(x + 1)(i)>, 0 <= i <= 2(s) a, of the chain ring GR(2(a), m)[x]/< x(2s) + 1 >. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field F-2m (i.e., a = 1), the symbol-pair distance distribution of constacyclic codes over F-2m verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length 2(s) over F-2m.

引用

页码：581 / 600

页数：20

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