On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6ps

Let
$p$
be an odd prime,
$s$
,
$m$
be positive integers such that
$p^{m}\equiv 2 \pmod 3$
. In this paper, using the relationship about Hamming distances between simple-root cyclic codes and repeated-root cyclic codes, the Hamming distance of all cyclic codes of length
$6p^{s}$
over finite field
$\mathbb F_{p^{m}}$
is obtained. All maximum distance separable (MDS) cyclic codes of length
$6p^{s}$
are established.