A design and a code invariant under the simple group Co3

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A self-orthogonal doubly-even (276, 23) code invariant under Conway's simple group Co3 is constructed. The minimum weight codewords form a 2-(276, 100, 1458) doubly transitive block-primitive design with block stabilizer isomorphic to the Higman-Sims simple group HS. More generally, the codewords of any given weight are single orbits stabilized by maximal subgroups of Co3. The restriction of the code on the complement of a minimum weight codeword is the (176, 22) code discovered by Calderbank and Wales as a code invariant under HS.

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Copyright © 1993 Published by Elsevier Inc. Publisher’s version of record: https://doi.org/10.1016/0097-3165(93)90045-A

Publication Title

Journal of Combinatorial Theory, Series A