Title

Self‐dual codes and the nonexistence of a quasi‐symmetric 2‐(37,9,8) design with intersection numbers 1 and 3

Authors

Masaaki Harada, Tohoku University
Akihiro Munemasa, Tohoku University
Vladimir Tonchev, Michigan Technological UniversityFollow

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.

Publisher's Statement

© 2017 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.21556

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