On b-symbol distance, Hamming distance and RT distance of Type 1 λ-constacyclic codes of length 8ps over 𝔽pm[u]/ uk

Let [Formula: see text] be a Type 1 unit in [Formula: see text] where [Formula: see text] is an odd prime, [Formula: see text] is a positive integer and [Formula: see text] In this paper, we give the complete structure of all Type 1 [Formula: see text]-constacyclic codes and their duals of length [Formula: see text] over the finite commutative chain ring [Formula: see text] in terms of their generator polynomials. Using this structure, we determine the Hamming distance and the Rosenbloom–Tsfasman (RT) distance of all Type 1 [Formula: see text]-constacyclic codes. For [Formula: see text] and a unit [Formula: see text] we determine the [Formula: see text] -symbol distances of all [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text] where [Formula: see text] As illustrations, we provide several [Formula: see text]-constacyclic codes with new parameters with respect to Hamming, RT and [Formula: see text]-symbol metrics. MDS codes are widely recognized for their optimal error-correction capability, and MDS [Formula: see text]-symbol codes are generalization of MDS codes. We found some MDS [Formula: see text]-symbol constacyclic codes of length [Formula: see text] over [Formula: see text] Additionally, for [Formula: see text] we provide a decoding algorithm for Type 1 constacyclic codes of length [Formula: see text] over [Formula: see text] with respect to the Hamming, RT and [Formula: see text]-symbol metrics.