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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| Authors: | Masaaki Harada Akihiro Munemasa Vladimir D. Tonchev |
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| Affiliation: | 1. Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, Japan;2. Department of Mathematical Sciences, Michigan Technological University Houghton, Michigan |
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| Abstract: | 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. |
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| Keywords: | quasi‐symmetric 2‐design self‐orthogonal code doubly even self‐dual code |
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