Symmetric 2-(36,15,6) designs with an automorphism of order two
Document Type
Article
Publication Date
6-17-2024
Department
Department of Mathematical Sciences
Abstract
Bouyukliev, Fack and Winne classified all 2- (Formula presented.) designs that admit an automorphism of odd prime order, and gave a partial classification of such designs that admit an automorphism of order 2. In this paper, we give the classification of all symmetric 2- (Formula presented.) designs that admit an automorphism of order two. It is shown that there are exactly (Formula presented.) nonisomorphic such designs, (Formula presented.) of which are self-dual designs. The ternary linear codes spanned by the incidence matrices of these designs are computed. Among these codes, there are near-extremal self-dual codes with previously unknown weight distributions.
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Rukavina, S.,
&
Tonchev, V.
(2024).
Symmetric 2-(36,15,6) designs with an automorphism of order two.
Journal of Combinatorial Designs.
http://doi.org/10.1002/jcd.21952
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/841