Repeated-Root Constacyclic Codes of Length $3p^s$ over the Finite Non-Chain Ring $\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$ and their Duals
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909561033588736 |
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| author | Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G |
| author_facet | Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G |
| contents | This study aims to determine the algebraic structures of $α$-constacyclic codes of length $3p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$, for a prime $p \neq 3.$ For the unit $α$, we consider two different instances: when $α$ is a cube in $\mathcal{R}$ and when it is not. Analyzing the first scenario is relatively easy. When $α$ is not a unit in $\mathcal{R}$, we consider several subcases and determine the algebraic structures of constacyclic codes in those cases. Further, we also provide the number of codewords and the duals of $α$-constacyclic codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Repeated-Root Constacyclic Codes of Length $3p^s$ over the Finite Non-Chain Ring $\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$ and their Duals Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G Combinatorics 11T71, 14G50 This study aims to determine the algebraic structures of $α$-constacyclic codes of length $3p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$, for a prime $p \neq 3.$ For the unit $α$, we consider two different instances: when $α$ is a cube in $\mathcal{R}$ and when it is not. Analyzing the first scenario is relatively easy. When $α$ is not a unit in $\mathcal{R}$, we consider several subcases and determine the algebraic structures of constacyclic codes in those cases. Further, we also provide the number of codewords and the duals of $α$-constacyclic codes. |
| title | Repeated-Root Constacyclic Codes of Length $3p^s$ over the Finite Non-Chain Ring $\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$ and their Duals |
| topic | Combinatorics 11T71, 14G50 |
| url | https://arxiv.org/abs/2412.17697 |