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Codes, designs and graphs from the Janko groups \(J_1\) and \(J_2\). (English) Zbl 0999.05010

J. Comb. Math. Comb. Comput. 40, 143-159 (2002); correction ibid. 64, 153 (2008).
Summary: We construct some codes, designs and graphs that have the first or second Janko group, \(J_1\) or \(J_2\), respecively, 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.

MSC:

05B05 Combinatorial aspects of block designs
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
94B05 Linear codes (general theory)
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