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On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24

机译:在与推定的极值有关的5设计中,其长度为24的倍数的双偶自对码

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摘要

By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal doubly even self-dual code of length 24m for . If , and , then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight .
机译:根据Assmus和Mattson定理,在长度为24m的极值双偶自对码中,每个非平凡权重的码字形成了一个自正交的5设计。在本文中,我们研究由自正交5设计与上述5设计相同的参数构造的代码。我们给出自正交5设计的一些参数,其存在与等价于长度为24m的极双偶自对偶代码的存在相同。如果和,则表明由权重码字生成了长度为24m的极双偶自对偶码。

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