Ternary codes from primitive representations of the group <i>PSL<sub>2</sub>(9)</i> and a new 2-(15,7,36) design

Abstract

In this paper, we construct, using computations withMagma, a ternary code C from a primitive permutation representation of degree 15 of the group PSL2(9) by Key-Moori Method 1. The code C is an optimal code invariant under the group S6. We consider the action of the automorphism group S6 on C and its dual. By taking the support of any codeword ? of weight l and orbiting it under S6, 1-(15, l, kl) designs are obtained, where kl = l|?S6 |/15. For any codeword, the structure of the stabilizer in S6 is determined and primitivity of S6 on each design is examined. It is shown that the complement of one of these designs is actually a new design D with parameters 2-(15, 7, 36). Moreover, Aut(D) ? S6.