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

Nikita Jain; Sucheta Dutt; Ranjeet Sehmi

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arXiv · 2303.07800

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

Nikita Jain·Sucheta Dutt·Ranjeet Sehmi

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Abstract

The rings $Z_{4}+\nu Z_{4}$ have been classified into chain rings and non-chain rings on the basis of the values of $\nu^{2} \in Z_{4}+\nu Z_{4}.$ In this paper, the structure of cyclic codes of arbitrary length over the rings $Z_{4}+\nu Z_{4}$ for those values of $\nu^{2}$ 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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Nikita Jain, Sucheta Dutt, Ranjeet Sehmi. 2023-03-14. Structure and Rank of Cyclic codes over a class of non-chain rings. https://arxiv.org/abs/2303.07800

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