Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56
Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56
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DOI：
10.1007/s10623-004-5657-6
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发表时间：
2006
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影响因子：
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通讯作者：
M. Harada
中科院分区：
文献类型：
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作者：
M. Harada
本文证明了自正交3-(56，12，65)设计的块-点关联矩阵的各行所生成的码是长度为56的双偶自对偶码。结果表明，用最小重量的码字生成一个长度为56的极值双偶自对偶码。我们还证明了存在一千多个不等价的双偶自对偶码[56，28，12]码。这一结果表明，3-(56，12，65)非同构自正交设计有一千多个。
In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56,12,65) design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand inequivalent extremal doubly-even self-dual [56,28,12] codes. This result shows that there are more than one thousand non-isomorphic self-orthogonal 3-(56,12,65) designs.