Hamming and Symbol-Pair Distances of Constacyclic Codes of Length $2p^s$ over $\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$

TL;DR

This paper determines the Hamming and symbol-pair distances of constacyclic codes of length 2p^s over a specific finite ring, advancing understanding of code properties in non-chain ring contexts.

Contribution

It explicitly computes Hamming and symbol-pair distances for constacyclic codes over a non-chain ring of length 2p^s, a novel extension in coding theory.

Findings

Hamming distances for the codes are fully characterized.

Symbol-pair distances for the codes are completely determined.

Results apply to codes over a non-chain ring with specific algebraic structure.

Abstract

Let $p$ be an odd prime. In this paper, we have determined the Hamming distances for constacyclic codes of length $2p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$. Also their symbol-pair distances are completely obtained.