In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using λ-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of self-dual codes. Applying this technique together with the building-up construction, we construct singly-even binary self-dual codes of lengths 56, 58, 64, 80 and 92 that were not known in the literature before. Singly-even self-dual codes of length 80 with $\beta \in \{2,4,5,6,8\}$ in their weight enumerators are constructed for the first time in the literature.

中文翻译：

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来自四循环结构的修改的长度为 56、58、64、80 和 92 的新二进制自对偶码

在这项工作中，我们提供了一种使用λ -循环矩阵在可交换 Frobenius 环上构造自对偶码的新技术。新结构是对著名的自对偶码四循环结构的修改而衍生出来的。将此技术与构建结构一起应用，我们构建了以前文献中未知的长度为 56、58、64、80 和 92 的单偶二进制自对偶代码。长度为 80 的单偶自对偶码$\beta \in \{2,4,5,6,8\}$ 在文献中首次构建了它们的权重枚举器。