Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual near MDS codes. In this paper, we not only give check matrices of dual codes of twisted generalized Reed-Solomon codes (TGRS codes) but also present the efficient and necessary condition of self-dual TGRS codes. Moreover, we construct several classes of self-dual MDS or self-dual near MDS 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（自对偶MDS码）和自对偶近MDS码在编码理论和实践中非常重要。因此，构建自对偶 MDS 或自对偶近 MDS 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)对偶码的校验矩阵，而且还给出了自对偶TGRS码的有效必要条件。此外，我们从 TGRS 代码构建了几类自对偶 MDS 或自对偶近 MDS 码。