A self-orthogonal doubly even code invariant under McL: 2

We examine a design D and a binary code C constructed from a primitive permutation representation of degree 275 of the sporadic simple group (ML)-L-c. We prove that Aut(C) = Aut(D) = (ML)-L-c : 2 and determine the weight distribution of the code and that of its dual. In Section 5, we show that for a word w(i) of weight i, where i is an element of {100, 112, 164, 176} the stabilizer ((ML)-L-c)(wi) is a maximal subgroup of (ML)-L-c. The words of weight 128 splits into three orbits C-(128)1, C-(128)2 and C-(128)3, and similarly the words of weights 132 produces the orbits C-(132)1 and C-(132)2. For w(i) is an element of {C-(128)1, C-(128)2, C-(132)1}, we prove that ((ML)-L-c)(wi) is a maximal subgroup of (ML)-L-c. Further in Section 6, we deal with the stabilizers ((ML)-L-c : 2)(wi) by extending the results of Section 5 to (ML)-L-c : 2. (c) 2004 Elsevier Inc. All rights reserved.