In this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings \(\mathbb {F}_{2}+u\mathbb {F}_{2}\) and \(\mathbb {F}_{4}+u\mathbb {F}_{4}\). We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables.

中文翻译：

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Frobenius环上群环的自对偶编码的双边框构造

在这项工作中，我们描述了来自群环的自对偶代码的双重边界构造。我们证明，这种构造对于阶为2 p的组有效，其中p是奇数，在环\（\ mathbb {F} _ {2} + u \ mathbb {F} _ {2} \）和\（\ mathbb {F} _ {4} + u \ mathbb {F} _ {4} \）。通过发现许多新的长度为64、68和80的二进制自对偶代码，我们证明了这种新结构的重要性。新代码及其相应的权重枚举数在几个表中列出。