The permutation group of affine-invariant extended cyclic codes

The extended cyclic codes of length p^m, p is a prime, which are invariant under the affine-group acting on F_pm, are called affine-invariant codes. Following results of Berger (1996, 1994), we present the formal expression of the permutation group of these codes. Afterwards we give several tools in order to determine effectively the group of a given code or of some infinite class of codes. We next prove, by studying some examples, that our tools are efficient. In the end, we give our main application, the permutation group of primitive BCH codes defined on any prime field