Bounds on the minimum distances of a class of q-ary images of qm-ary irreducible cyclic codes

Let V=(n, k:) be an irreducible cyclic code over F_q^m, the finite field of q^m elements. Let α_ be a basis of F_q^m over F_q. Under the simplifying assumption (n,q)=1, it is shown that dα_(V), the q-ary image of V with respect to α, is decomposable into the direct sum of a fixed number of irreducible quasicyclic codes. This characterization allow us to obtain a lower bound on the minimum distance of dα_(V) by determining a lower bound on the number of not- blocks in a typical codeword of dα_(V), for four specific subclasses of codes.