New Results on Self-Dual Generalized Reed-Solomon Codes

This paper focuses on constructions of MDS self-dual codes from (extended) generalized Reed-Solomon (GRS) codes. Let q = r {2} be an odd prime power. We show that, there exists a q -ary self-dual (extended) GRS code for each even length in the range [{2r,3r-3}] , and for each singly even length in the range [3r-1,4r]. This extends the only known consecutive range [2,2r] to [{2,3r-3}] for this case. Furthermore, our general constructions provide many MDS self-dual codes with new parameters which, to the best of our knowledge, were not reported before.