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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… Click to show full 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.
Keywords:
quasi symmetric;
symmetric design;
design intersection;
self dual;
intersection numbers
Journal Title: Journal of Combinatorial Designs
Year Published: 2017
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Journal Title: Journal of Combinatorial Designs
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!