The automorphism groups of BCH codes and of some affine-invariant codes over extension fields

Affine-invariant codes are extended cyclic codes of length p(m) invariant under the affine-group acting on F-p(m). This class of codes includes codes of great interest such as extended narrow-sense BCH codes. In recent papers, we classified the automorphism groups of affine-invariant codes [2], [5]. We derive here new results, especially when the alphabet field is an extension field, by expanding our previous tools. In particular we complete our results on BCH codes, giving the automorphism groups of extended narrow-sense BCH codes defined over any extension field.