On the Lattice of Cyclic Linear Codes Over Finite Chain Rings

Abstract

Let $\text{R}$ be a commutative finite chain ring of invariants $(q,s).$ In this paper, the trace representation of any free cyclic $\text{R}$-linear code of length $\ell ,$ is presented, via the $q$-cyclotomic cosets modulo $\ell ,$ when $\text{gcd}(\ell ,q)=1.$ The lattice $\left(\text{Cy}(\text{R},\ell ),+,\cap \right)$ of cyclic $\text{R}$-linear codes of length $\ell ,$ is investigated. A lower bound on the Hamming distance of cyclic $\text{R}$-linear codes of length $\ell ,$ is established. When $q$ is even, a family of MDS and self-orthogonal $\text{R}$-linear cyclic codes, is constructed.

arXiv admin note: substantial text overlap with arXiv:1701.08736

Cited by in corpus (1)

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