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

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 $\mathcal{R}=\frac{{\mathbb{F}}_{p^m}[u,v]}{⟨u^2,v^2,uv-vu⟩}$. Also their symbol-pair distances are completely obtained.