Repeated-root constacyclic codes of length 4ℓmpn

Constacyclic codes form a well-known class of linear codes, and are generalizations of cyclic and negacyclic codes. In this paper, we determine generator polynomials of all constacyclic codes of length 4ℓmpn4ℓmpn over the finite field FqFq with q   elements, where p,ℓp,ℓ are distinct odd primes, q is a power of p   and m,nm,n are positive integers. We also determine their dual codes, and list all self-dual constacyclic codes of length 4ℓmpn4ℓmpn over FqFq.