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.
- doubly even self-dual code
- quasi-symmetric 2-design
- self-orthogonal code
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics