New LCD MDS codes constructed from generalized Reed-Solomon codes

作者:Shi, Xueying; Yue, Qin*; Yang, Shudi
来源:Journal of Algebra and Its Applications, 2019, 18(8): 1950150.
DOI:10.1142/S0219498819501500

摘要

Maximum distance separable codes with complementary duals (LCD MDS codes) are very important in coding theory and practice, and have attracted a lot of attention. In this paper, we focus on LCD MDS codes constructed from generalized Reed-Solomon (GRS) codes over a finite field with odd characteristic. We detail two constructions of new LCD MDS codes, using invertible matrices and the roots of three classes of polynomials, respectively.