Structure and Rank of Cyclic codes over a class of non-chain rings

2023/03/14 by Nikita Jain, Jain, Nikita, Sucheta Dutt +3
Computer Science · Medicine · #Coding theory and cryptography #Cancer Mechanisms and Therapy

paper · pdf · doi:10.48550/arxiv.2303.07800

Abstract

The rings Z₄+νZ₄ have been classified into chain rings and non-chain rings on the basis of the values of ν² ∈ Z₄+νZ₄. In this paper, the structure of cyclic codes of arbitrary length over the rings Z₄+νZ₄ for those values of ν² for which these are non-chain rings has been established. A unique form of generators of these codes has also been obtained. Further, rank and cardinality of these codes have been established by finding minimal spanning sets for these codes.

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