Codes, Designs and Graphs from the Janko Groups $J_1$ and $J_2$

Abstract

We construct some codes, designs and graphs that have the first or second Janko group, $J_1$ or $J_2$, respectively, acting as an automorphism group. We show computationally that the full automorphism group of the design or graph in each case is $J_1$, $J_2$ or ${\overline{J}}_2$, the extension of $J_2$ by its outer automorphism, and we show that for some of the codes the same is true.