Repeated-root constacyclic codes of length 3lps and their dual codes

Let p≠3p≠3 be any prime and l≠3l≠3 be any odd prime with gcd⁡(p,l)=1gcd⁡(p,l)=1. The multiplicative group Fq⁎=〈ξ〉 can be decomposed into mutually disjoint union of gcd⁡(q−1,3lps)gcd⁡(q−1,3lps) cosets over the subgroup 〈ξ3lps〉〈ξ3lps〉, where ξ   is a primitive (q−1)(q−1)th root of unity. We classify all repeated-root constacyclic codes of length 3lps3lps over the finite field FqFq into some equivalence classes by this decomposition, where q=pmq=pm, s and m   are positive integers. According to these equivalence classes, we explicitly determine the generator polynomials of all repeated-root constacyclic codes of length 3lps3lps over FqFq and their dual codes. Self-dual cyclic codes of length 3lps3lps over FqFq exist only when p=2p=2. We give all self-dual cyclic codes of length 3⋅2sl3⋅2sl over F2mF2m and their enumeration. We also determine the minimum Hamming distance of these codes when gcd⁡(3,q−1)=1gcd⁡(3,q−1)=1 and l=1l=1.