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：

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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。