Constacyclic codes over Z2 [u]/⟨u2⟩ x Z2 [u]/⟨u3⟩ and the MacWilliams identities

被引：0

作者：

Sagar, Vidya ^{[1
]}

Yadav, Ankit ^{[1
]}

Sarma, Ritumoni ^{[1
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, Delhi, India

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2024年

关键词：

Constacyclic code; Gray map; Quasi-cyclic code; Weight enumerator; MacWilliams identities; LINEAR CODES; CYCLIC CODES; EUCLIDEAN WEIGHTS; RINGS; LEE;

D O I：

10.1007/s00200-024-00662-6

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this article, we deal with additive codes over the Frobenius ring R2R3 := Z(2)[u]/< u(2)> x Z(2)[u]/< u(3)>. First, we study constacyclic codes over R-2 and R-3 and find their generator polynomials. With the help of these generator polynomials, we determine the structure of constacyclic codes over R2R3. We use Gray maps to show that constacyclic codes over R2R3 are essentially binary generalized quasi-cyclic codes. Moreover, we obtain a number of binary codes with good parameters from these R2R3-constacyclic codes. Besides, several weight enumerators are computed, and the corresponding MacWilliams identities are established.

引用

页数：30

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