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Binary extremal self-dual codes of length 60 and related codes

机译:长度为60的二进制极值自对码和相关码

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摘要

We give a classification of four-circulant singly even self-dual [60, 30, d] codes for and 12. These codes are used to construct extremal singly even self-dual [60, 30, 12] codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual [60, 30, 12] codes, we also construct optimal singly even self-dual [58, 29, 10] codes with weight enumerator for which no optimal singly even self-dual code was previously known to exist. Finally, we give some restriction on the possible weight enumerators of certain singly even self-dual codes with shadow of minimum weight 1.
机译:我们给出了和的四循环单偶对偶[60,30,d]代码的分类。这些代码用于构造带有权重枚举的极个别单偶对偶[60,30,12]代码。以前不存在极高的单个甚至双对偶代码。从极个别单双[60、30、12]代码中,我们还构造了具有权重枚举器的最佳单一单双[58、29、10]代码,以前没有已知最佳单一双偶的代码。存在。最后,我们对某些具有最小权重1的阴影的某些甚至单自对码的权重枚举数进行了一些限制。

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