The main aim of coding theory is to construct codes that are easier to encode and decode, can correct or at least detect many errors, and contain a sufficiently large number of codewords. To study error-detecting and error-correcting properties of a code with respect to various communication channels, several metrics (e.g. Hamming metric, Lee metric, Rosenbloom-Tsfasman (RT) metric, symbol-pair metric, etc.) have been introduced and studied in coding theory.
In this talk, we will establish algebraic structures of all repeated-root constacyclic codes of prime power lengths over finite commutative chain rings. Using their algebraic structures, we will determine Hamming distances, b-symbol distances, RT distances, and RT weight distributions of these codes. As an application of these results, we will identify MDS (maximum-distance separable) Hamming, MDS b-symbol and MDS RT codes within this particular class of constacyclic codes. We will also present an algorithm to decode these codes with respect to the Hamming, symbol-pair and RT metrics.