Codes, Designs and Graphs from the Janko Groups \(J_1\) and \(J_2\)

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 \(\bar{J}_2\), the extension of \(J_2\) by its outer automorphism, and we show that for some of the codes the same is true.