The minimal spanning sets of constacyclic codes over polynomial residue rings

The minimal spanning sets and ranks of (1+λu) constacyclic codes with an arbitrary length N=pen over R=Fpm［u］/〈uk〉 were investigated, where uk=0 and λ is a unit of R. Specifically, the case with k=2 and λ=1 was given, while a small mistake about the minimal spanning sets in [Abular T, Siap I. Constacyclic codes over F2+uF2. Journal of the Franklin Institute, 2009, 345: 520-529] was pointed out. Furthermore, based on the analysis of the equivalence between cyclic codes and constacyclic codes over R, the generator polynomials and minimal spanning sets of some other constacyclic codes over R were obtained. As a consequence, the generator polynomials and minimal spanning sets of (1+ζu2) constacyclic codes with odd length and length N≡2(mod 4) over F2m［u］/〈u3〉 were given for any ζ∈F*2m.