Codes over $\mathbb{Z}_{p}[u]/{\langle u^r \rangle}\times\mathbb{Z}_{p}[u]/{\langle u^s \rangle}$

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Ismail Aydogdu¹ 

[1] Department of Mathematics, Yildiz Technical University

关键词: Linear codes;    Self-dual codes;    Z_2Z_2[u]-linear codes;    Z_p[u^r;    u^s ]-linear codes;   

DOI  :  10.13069/jacodesmath.514339

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

In this paper we generalize Z2Z2[u]-linear codes to codes over Zp[u]/huri × Zp[u]/husi where p is aprime number and ur = 0 = us. We will call these family of codes as Zp[ur, us]-linear codes whichare actually special submodules. We determine the standard forms of the generator and parity-checkmatrices of these codes. Furthermore, for the special case p = 2, we define a Gray map to explore thebinary images of Z2[ur, us]-linear codes. Finally, we study the structure of self-dual Z2[u2, u3]-linearcodes and present some examples.

【 授权许可】

CC BY