An extremal ternary self-dual [28, 14, 9] code with a trivial automorphism group
An extremal ternary self-dual [28, 14, 9] code with a trivial automorphism group
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具有平凡自同构群的极值三元自对偶 [28, 14, 9] 码
DOI：
10.1016/s0012-365x(01)00041-3
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Harada
中科院分区：
文献类型：
--
作者：
M. Harada
在本文中，我们通过构造这样一个长度为 28 的码，证明了具有平凡自同构群的极值三元自对偶码的最小长度为 28。该码是具有平凡自同构群的极值三元自对偶码的第一个例子。还构造了具有平凡自同构群的极值三元自对偶[32,16,9]码。通过构造 A 从代码中获得了最小范数为 3 和平凡自同构群的 32 维奇幺模格。
In this paper, we show that the smallest length for which there is an extremal ternary self-dual code with a trivial automorphism group is 28 by constructing such a code of length 28. This code is the first example of extremal ternary self-dual codes with trivial automorphism groups. An extremal ternary self-dual [32,16,9] code with a trivial automorphism group is also constructed. A 32-dimensional odd unimodular lattice with minimum norm 3 and a trivial automorphism group is obtained from the code by Construction A.