Code–checkable group rings

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Noha Abdelghany¹  Nefertiti Megahed¹ 

[1] Department of Mathematics, Faculty of Science, Cairo University

关键词: Group rings;    Pseudo-morphic rings;    A-by-B groups;    Checkable codes;    Pseudo-morphic group rings;   

DOI  :  10.13069/jacodesmath.284939

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

A code over a group ring is defined to be a submodule of that group ring. For a code C over agroup ring RG, C is said to be checkable if there is v ∈ RG such that C = {x ∈ RG : xv = 0}. In [6],Jitman et al. introduced the notion of code-checkable group ring. We say that a group ring RG iscode-checkable if every ideal in RG is a checkable code. In their paper, Jitman et al. gave a necessaryand sufficient condition for the group ring FG, when F is a finite field and G is a finite abelian group,to be code-checkable. In this paper, we give some characterizations for code-checkable group rings formore general alphabet. For instance, a finite commutative group ring RG, with R is semisimple, iscode-checkable if and only if G is π0-by-cyclic π; where π is the set of noninvertible primes in R. Also,under suitable conditions, RG turns out to be code-checkable if and only if it is pseudo-morphic.

【 授权许可】

CC BY