New Results on Self-Dual Generalized Reed-Solomon Codes
Yu Ning, Zuo Ye, Gennian Ge, Fuyou Miao, Yan Xiong, Xiande Zhang · IEEE Transactions on Information Theory · 2021
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.