In this work, we describe a construction for self-dual codes in which we employ group rings and reverse circulant matrices. By applying the construction directly over different alphabets, and by employing the well known extension and neighbor methods we were able to obtain extremal binary self-dual codes of different lengths of which some have parameters that were not known in the literature before. In particular, we constructed three new codes of length 64, twenty-two new codes of length 68, twelve new codes of length 80 and four new codes of length 92.

中文翻译：

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从群环和逆循环矩阵构造自对偶码

在这项工作中，我们描述了一种自对偶代码的构造，其中我们使用了群环和反向循环矩阵。通过直接在不同的字母上应用构造，并通过使用众所周知的扩展和邻居方法，我们可以获得具有不同长度的极值二进制自对偶代码，其中一些参数具有以前文献中所不知道的。特别是，我们构造了三个新的长度为64的代码，二十两个新的长度为68的代码，十二个新的长度为80的代码和四个新的长度为92的代码。