quaternary codes and a class of 2-designs invariant under the group a₈

In this paper, we use the key-moori method 1 and construct a quaternary code c8 from a primitive representation of the group psl2(9) of degree 15. we see that c8 is a self-orthogonal even code with the automorphism group isomorphic to the alternating group a₈. it is shown that by taking the support of any codeword ω of weight l in c₈ or c₈⊥, and orbiting it under a8, a 2-(15, l, λ) design invariant under the group a8 is obtained, where λ = (l )|ωa8 |/(15). a number of these designs have not been known before up to our best knowledge. the structure of the stabilizers (a8)ω is determined and moreover, primitivity of a8 on each design is examined.