Affine invariant extended cyclic codes over Galois rings

Recently, Blackford and Ray-Chaudhuri used transform domain techniques to permutation groups of cyclic codes over Galois rings. They used the same technique to rind a set of necessary and sufficient conditions for extended cyclic codes of length 2(m) over any subring of GR (4, m) to be affine invariant. Here, we use the same technique to find a set of necessary and sufficient conditions for extended cyclic codes of length p(m) over any subring of GR (p', m) to be affine invariant, for e = 2 with arbitrary p and for p = 2 with arbitrary e. These are used to find two new classes of affine invariant Bose-Chaudhuri-Hocquenghem (BCH) and generalized Reed-Muller (GRM) codes over Z(2e) for arbitrary e and a class of affine invariant BCH codes over Z(p2) for arbitrary prime p.