On constacyclic codes over a class of non-chain rings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914866367823872 |
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| author | Jain, Nikita Dutt, Sucheta Sehmi, Ranjeet |
| author_facet | Jain, Nikita Dutt, Sucheta Sehmi, Ranjeet |
| contents | In this paper, a unique form of generators of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_θ}}=Z_{4}+νZ_{4}, ν^{2}=θ\in Z_{4}+νZ_{4}$ has been obtained. Further, rank and cardinality of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_θ}}$ 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 $\mathtt{R_{_θ}}$ to be reversible have been determined. Examples have also been presented in support of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On constacyclic codes over a class of non-chain rings Jain, Nikita Dutt, Sucheta Sehmi, Ranjeet Commutative Algebra In this paper, a unique form of generators of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_θ}}=Z_{4}+νZ_{4}, ν^{2}=θ\in Z_{4}+νZ_{4}$ has been obtained. Further, rank and cardinality of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_θ}}$ 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 $\mathtt{R_{_θ}}$ to be reversible have been determined. Examples have also been presented in support of our results. |
| title | On constacyclic codes over a class of non-chain rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2407.08193 |