Bulletin of the American Mathematical Society

ABSTRACT. There are 26 distinct indecomposable self-dual codes of length 24 over GF(2), including unique codes of minimum weights 8 and 6, whose groups are, respectively, the Mathieu group M24 and the maximal subgroup of index 1771 in M^> For each code we give the order of its group, the number of equivalent codes, and its weight distribution. 1. Introduction. An [n, k] code C is a ^-dimensional subspace of the vector space of all «-tuples of O's and l's with mod 2 addition. The dual code C 1 = {u: u • v = 0 for all v G C} is an [n, n- k] code. C is self-orthogonal if C C C 1, self-dual if C — C 1. Self-dual codes exist whenever