On $b$ -Symbol Distances of Repeated-Root Constacyclic Codes

Let
$p$
be a prime,
$s$
be a positive integer, and let
$b$
be an integer satisfying
$2 \leq b < p^{s}$
. In this paper, we obtain
$b$
-symbol distances of all repeated-root constacyclic codes of length
$p^{s}$
over finite fields. Using this result, we determine
$b$
-symbol distances of all repeated-root constacyclic codes of length
$p^{s}$
over finite commutative chain rings. We also list all MDS
$b$
-symbol repeated-root constacyclic codes of length
$p^{s}$
over finite fields, and all MDS
$b$
-symbol repeated-root constacyclic codes of length
$p^{s}$
over finite commutative chain rings in general.