In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using $\lambda$-circulant matrices. The new constructions are derived as modifications of various well-known circulant constructions of self-dual codes. Applying these constructions together with the building-up construction, we construct many new best known quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40.

中文翻译：

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长度为26、32、36、38和40的第四代Hermitian自对码，来自于众所周知的循环结构的修改

在这项工作中，我们给出了使用$ \ lambda $循环矩阵在具有非平凡的对合自同构的可交换Frobenius环上构造Hermitian自对偶代码的三种新技术。这些新构造是对自对偶编码的各种众所周知的循环构造的修改而得出的。将这些构造与组合构造一起应用，我们构造了许多新的最著名的四元Hermitian自对偶代码，其长度分别为26、32、36、38和40。