Skew-cyclic and skew-quasi-cyclic codes over a general infinite family of rings

Articles in Press

Document Type : Original paper

Authors

1 Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, 40132, Indonesia

2 Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia

3 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Mataram, Indonesia

Abstract

We study structural properties of cyclic codes, and their generalization, over a general infinite family of rings, namely the ring Rk defined by R[v1,v2,…,vk] with conditions vi2=vi, for i∈[1,k]\ZZ, where R is any finite commutative Frobenius ring. We derived necessary and sufficient condition for the codes to be cyclic, quasi-cyclic, skew-cyclic as well as to be quasi-skew-cyclic. As an application, we constructed optimal linear codes over \ZZ4 as a Gray images of our codes.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 07 July 2025

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