Designs, Codes and Cryptography ( IF 1.4 ) Pub Date : 2021-07-12 , DOI: 10.1007/s10623-021-00910-7 Daitao Huang 1, 2 , Yongfeng Niu 1, 2 , Qin Yue 2, 3 , Xia Li 2, 3
Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS (NMDS) codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual NMDS codes. In this paper, we not only give parity-check matrices of dual codes of twisted generalized Reed–Solomon codes (TGRS codes) but also present a sufficient and necessary condition of self-dual TGRS codes over \({\mathbb {F}}_q\) with q an odd prime. Moreover, we construct several classes of self-dual MDS or self-dual NMDS codes from TGRS codes.
中文翻译:
来自扭曲广义 Reed-Solomon 码的 MDS 或 NMDS 自对偶码
自对偶最大距离可分码(self-dual MDS码)和自对偶近MDS(NMDS)码在编码理论和实践中非常重要。因此,构建自双 MDS 或自双 NMDS 代码是很有趣的。在本文中,我们不仅给出了扭曲广义 Reed-Solomon 码(TGRS 码)的对偶码的奇偶校验矩阵,而且还给出了自对偶 TGRS 码在\({\mathbb {F}} _q\),其中q是奇素数。此外,我们从 TGRS 代码构建了几类自双 MDS 或自双 NMDS 代码。