Self‐dual codes and the nonexistence of a quasi‐symmetric 2‐(37,9,8) design with intersection numbers 1 and 3
Document Type
Article
Publication Date
3-21-2017
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.
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Harada, M.,
Munemasa, A.,
&
Tonchev, V.
(2017).
Self‐dual codes and the nonexistence of a quasi‐symmetric 2‐(37,9,8) design with intersection numbers 1 and 3.
Journal of Combinatorial Designs,
25(10), 469-476.
http://doi.org/10.1002/jcd.21556
Retrieved from: https://digitalcommons.mtu.edu/math-fp/80
Publisher's Statement
© 2017 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.21556