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A Characterization of Designs Related to an Extremal Doubly-Even Self-Dual Code of Length 48
Masaaki Harada1, Akihiro Munemasa2 and Vladimir D. Tonchev3
1Department of Mathematical Sciences, Yamagata University, Yamagata 990–8560, Japan
mharada@sci.kj.yamagata-u.ac.jp
2Graduate School of Information Sciences, Tohoku University, Sendai 980–8579, Japan
munemasa@math.is.tohoku.ac.jp
3Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
tonchev@mtu.edu
Annals of Combinatorics 9 (2) p.89-198 June, 2005
AMS Subject Classification: 05B05, 94B05
Abstract:
The uniqueness of a binary doubly-even self-dual [48, 24, 12] code is used to prove that a self-orthogonal 5-(48, 12, 8) design, as well as some of its derived and residual designs, including a quasi-symmetric 2-(45, 9, 8) design, are all unique up to isomorphism.
Keywords: self-orthogonal design, quasi-symmetric design, self-orthogonal code, extremal selfdual code

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