engleski

New symmetric 2-(71,15,3) designs

A symmetric 2-(v, k, lambda) design is called a triplane. In this paper we construct two triplanes of order twelve, i.e., symmetric 2-(71, 15, 3) designs, from the bonary codes of the previously known triplanes. All 146 previously known triplanes of order twelve, i.e., symmetric 2- (71, 15, 3) designs, admit an action of an automorphism of order three, while these two newly constructed triplanes have full automorphism groups that are isomorphic to the elementary abelian group of order eight. Furthermore, possible actions of automorphisms of prime order on a triplane of order twelve are studied.

symmetric design, triplane, automorphism group, linear code

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