Some new classes of MDS and AMDS symbol-pair constacyclic codes of length 4p and symbol-pair distance up to 8

The concept of symbol-pair coding stems from the observation that in many practical communication and storage systems, errors do not always occur as isolated corruptions of single symbols. Instead, they often appear in bursts or clusters, affecting consecutive symbols. Symbol-pair codes address this by encoding and processing overlapping pairs of symbols rather than individual symbols. This representation allows the coding scheme to detect and correct error patterns that would be more difficult to handle using traditional single-symbol codes, thereby enhancing error correction performance in channels prone to such clustered error behavior. In this paper, we will explicitly provide a construction of some new MDS and AMDS symbol-pair constacyclic codes of length [Formula: see text] and symbol-pair distance up to [Formula: see text]. This results in a useful collection of optimal symbol-pair constacyclic codes applicable directly in various real-world scenarios.