Symmetric 2-(36,15,6) designs with an automorphism of order two

Document Type

Article

Publication Date

1-1-2024

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

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