Self-Dual Codes and the Nonexistence of a Quasi-Symmetric 2-(37,9,8) Design with Intersection Numbers 1 and 3
Self-Dual Codes and the Nonexistence of a Quasi-Symmetric 2-(37,9,8) Design with Intersection Numbers 1 and 3
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自对偶码和交点编号为 1 和 3 的拟对称 2-(37,9,8) 设计的不存在
DOI：
10.1002/jcd.21556
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Tonchev Vladimir D.
中科院分区：
文献类型：
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作者：
Harada Masaaki;Munemasa Akihiro;Tonchev Vladimir D.
证明了具有交点数为1和3的拟对称2‐（37,9,8）设计的关联矩阵所对应的二元线性码必须包含在长度为40的极值双偶自对偶码中。利用长度为40的极值双偶自对偶码的分类，证明了具有交集数为1和3的拟对称2‐（37,9,8）设计不存在。
We prove that a certain binary linear code associated with the incidence matrix of a quasi‐symmetric 2‐(37, 9, 8) design with intersection numbers 1 and 3 must be contained in an extremal doubly even self‐dual code of length 40. Using the classification of extremal doubly even self‐dual codes of length 40, we show that a quasi‐symmetric 2‐(37, 9, 8) design with intersection numbers 1 and 3 does not exist.