On the binary codes of length 552 which admit the simple group Co3 as a transitive permutation group

Abstract

In this this paper all binary codes of length 552 which admit the sporadic simple group Co3 as an imprimitive transitive permutation group are determined. Our aim is to understand the results also by using theoretical arguments and to discuss the combinatorial properties of the codes as well as their relation to some special properties of the Leech lattice group Co3. For all codes (with two exceptions) we obtain the weight enumerators and in many interesting cases the classification of codewords under the action of the group of code automorphisms Co3. The exceptional codes are both self-dual and have minimum weight 12.