On a class of constacyclic codes and MDS code construction over 𝔽pm[u,v] 〈u2−δu,v2−γv,uv−vu〉

Let [Formula: see text] denote a finite field, where [Formula: see text] is a prime and [Formula: see text] is a positive integer. In this paper, we study idempotent decomposition of the finite, commutative, non-local ring, [Formula: see text], where [Formula: see text]. This paper consists of the structure of [Formula: see text]-constacyclic (CC) codes over [Formula: see text], where [Formula: see text]. The structure of dual of CC codes is used to determine the Euclidean hull of such codes. Then, the Hamming distance and symbol-pair distance for the [Formula: see text]-CC codes of length [Formula: see text] over [Formula: see text] is determined. Additionally, conditions for repeated root [Formula: see text]-CC code to be maximal distance separable (MDS) in terms of Hamming distance and symbol-pair distance are provided. Finally, we present examples of several linear and symbol-pair codes some of which are MDS with respect to Hamming and symbol-pair distance.