A note on the constructions of MDS self-dual codes

摘要

Due to the nice structures of maximum distance separable (MDS) codes and self-dual codes, it is worth studying MDS self-dual codes. It is easy to see that parameters of a MDS self-dual code are completely determined by the code length. The main problem in this topic is to determine existence of q-ary MDS self-dual codes of various lengths. The problem is completely solved when q is even. This paper focuses on the case that q is odd. We generalize the technique in [13] and construct several classes of MDS self-dual codes via generalized Reed-Solomon codes and extended generalized Reed-Solomon codes.