New MDS Euclidean Self-Orthogonal Codes

作者：Fang, Xiaolei; Liu, Meiqing; Luo, Jinquan^*

来源：IEEE Transactions on Information Theory, 2021, 67(1): 130-137.

DOI：10.1109/TIT.2020.3020986

• MDS code
• Euclidean (almost) self-dual code
• Euclidean self-orthogonal code
• generalized Reed-Solomon (GRS) code
• extended generalized Reed-Solomon (GRS) code

In this paper, two criterions of MDS Euclidean self-orthogonal codes are presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via the criterions. In particular, among our constructions, for large square q, about 1/8 . q new MDS Euclidean (almost) self-dual codes over Fq can be produced. Moreover, we can construct about 1/4 . q new MDS Euclidean self-orthogonal codes with different even lengths n and dimension n/2 - 1.