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

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.