Hamming and Symbol-Pair Distances of Constacyclic Codes of Length 2p^s over (Formula presented.)

Let (Formula presented.), where p is an odd prime and m is a positive integer. For a unit (Formula presented.) in (Formula presented.), (Formula presented.) -constacyclic codes of length (Formula presented.) over (Formula presented.) are ideals of (Formula presented.), where s is a positive integer. The structure of (Formula presented.) -constacyclic codes are classified on the distinct cases for the unit (Formula presented.) : when (Formula presented.) is a square in (Formula presented.) and when it is not. In this paper, for all such (Formula presented.) -constacyclic codes, the Hamming distances are determined using this structure. In addition, their symbol-pair distances are obtained. The symmetry property of Hamming and symbol-pair distances makes analysis easier and maintains consistency by guaranteeing that the distance between codewords is the same regardless of their order. As symmetry preserves invariant distance features across transformations, it improves error detection and correction.