Structure of some classes of repeated-root constacyclic codes of length 2Kℓmpn

Abstract

Abstract Let F q be the finite field of order q , where q is a power of an odd prime p , and p , l are distinct odd primes, and m , n , K are positive integers. In this paper, the multiplicative group F q ∗ = F q ∖ { 0 } is decomposed into mutually disjoint union of gcd ( 2 K l m , q − 1 ) cosets of the cyclic group generated by ξ 2 K l m p n , where ξ is a primitive element of F q . With the help of this decomposition, all constacyclic codes of length 2 K l m p n over F q are classified into gcd ( 2 K l m , q − 1 ) disjoint classes. Accordingly, generator polynomials of constacyclic codes of length 2 K l m p n over the finite field F q and their duals are explicitly determined in the cases, when q ≡ ± 1 ( mod 2 K ) . And also some complementary-dual, self-orthogonal, self-dual, dual-containing constacyclic codes of length 2 K l m p n over F q are determined.