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arXiv · 2412.17697

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

Divya Acharya·Prasanna Poojary·Vadiraja Bhatta G R
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Abstract

This study aims to determine the algebraic structures of $\alpha$-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 $\alpha$, we consider two different instances: when $\alpha$ is a cube in $\mathcal{R}$ and when it is not. Analyzing the first scenario is relatively easy. When $\alpha$ 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 $\alpha$-constacyclic codes.

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Divya Acharya, Prasanna Poojary, Vadiraja Bhatta G R. 2024-12-23. 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. https://doi.org/10.1142/s179383092550065x

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