Self-dual codes, which are codes that are equal to their orthogonal, are a widely studied family of codes. Various techniques involving circulant matrices and matrices from group rings have been used to construct such codes. Moreover, families of rings have been used, together with a Gray map, to construct binary self-dual codes. In this paper, we introduce a new bordered construction over group rings for self-dual codes by combining many of the previously used techniques. The purpose of this is to construct self-dual codes that were missed using classical construction techniques by constructing self-dual codes with different automorphism groups. We apply the technique to codes over finite commutative Frobenius rings of characteristic 2 and several group rings and use these to construct interesting binary self-dual codes. In particular, we construct some extremal self-dual codes of length 64 and 68, constructing 30 new extremal self-dual codes of length 68.

自对偶代码是等于其正交的代码，是广泛研究的代码家族。已经使用了涉及循环矩阵和来自群环的矩阵的各种技术来构造这样的代码。而且，已经使用了环族以及格雷图来构造二进制自对偶码。在本文中，我们结合了许多以前使用的技术，为自对偶编码引入了一种新的有界环在群环上。这样做的目的是通过构造具有不同自同构群的自对码来构造使用经典构造技术遗漏的自对码。我们将该技术应用于特征2的有限可交换Frobenius环和几个群环的编码，并使用它们构造有趣的二进制自对偶编码。尤其是，