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arXiv · 2407.08193

On constacyclic codes over a class of non-chain rings

Nikita Jain·Sucheta Dutt·Ranjeet Sehmi
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Abstract

In this paper, a unique form of generators of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}=Z_{4}+\nu Z_{4}, \nu^{2}=\theta \in Z_{4}+\nu Z_{4}$ has been obtained. Further, rank and cardinality of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}$ have been obtained by determining a minimal spanning set of the code. Also, necessary and sufficient conditions for a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}$ to be reversible have been determined. Examples have also been presented in support of our results.

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Nikita Jain, Sucheta Dutt, Ranjeet Sehmi. 2024-07-11. On constacyclic codes over a class of non-chain rings. https://arxiv.org/abs/2407.08193

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