MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual codes with new length by using generalized Reed-Solomon codes and extended generalized Reed-Solomon codes as the candidates of MDS codes and taking their evaluation sets as a union of cyclotomic classes. The conditions on such MDS codes being self-dual are expressed in terms of cyclotomic numbers.

中文翻译：

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基于分圆法构造MDS自对偶码

近年来，有限域上的 MDS 自对偶码因其对编码理论的理论兴趣以及在密码学和组合学中的应用而引起了很多关注。在本文中，我们通过使用广义 Reed-Solomon 码和扩展广义 Reed-Solomon 码作为 MDS 码的候选，并将它们的评估集作为分圆类的并集，提出了一系列新长度的 MDS 自对偶码。这种自对偶的 MDS 码的条件用圈数表示。