1. New Results on Self-Dual Generalized Reed-Solomon Codes.
- Author
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Ning, Yu, Ye, Zuo, Ge, Gennian, Miao, Fuyou, Xiong, Yan, and Zhang, Xiande
- Subjects
RESEARCH & development ,REED-Solomon codes ,LINEAR codes ,TELECOMMUNICATION satellites - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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