In this paper, we provide new methods and algorithms to construct Euclidean self-dual codes over large finite fields. With the existence of a dual basis, we study dual preserving linear maps, and as an application, we use them to construct self-orthogonal codes over small finite prime fields using the method of concatenation. Many new optimal self-orthogonal and self-dual codes are obtained.

中文翻译：

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关于欧几里得自对偶码和等距码

在本文中，我们提供了在大型有限域上构造欧几里得自对偶码的新方法和算法。在对偶基的存在下，我们研究了对偶保持线性映射，并作为一个应用，使用它们在小的有限素域上用串联的方法构造自正交码。得到了许多新的最优自正交和自对偶码。