A subclass of q^m -ary Reed–Solomon codes and decoding of some rational GAG-codes

In this paper, we introduce the notion of preserving distance codes (PD-codes) and we propose a decoding algorithm, using the error correcting pairs, for these codes in a particular case, without involving the duality. Then, we give a subclass of Reed Solomon codes which are primitive, and we give conditions for which these codes are PD-codes. Finally, we determine the minimum distance of some GAG-codes.