The minimum Hamming distances of repeated-root cyclic codes of length $$6p^s$$6ps and their MDS codes

In this paper, let p be a prime with $$p\ge 7$$ . We determine the weight distributions of cyclic codes of length 6 over $$\mathbb {F}_q$$ and the minimum Hamming distances of all repeated-root cyclic codes of length $$6p^s$$ over $$\mathbb {F}_q$$ , where q is a power of p and s is an integer. Furthermore, we find all maximum distance separable codes of length $$6p^s$$ .