Designs and binary codes from maximal subgroups and conjugacy classes of the mathieu group m11

By using a method of constructing block-primitive and point-transitive 1-designs, in this paper we determine all block-primitive and point-transitive 1-(v, k, λ)-designs from the maximal subgroups and the conjugacy classes of elements of the small Mathieu group M11. We examine the properties of 1-(v, k, λ)-designs and construct the codes defined by the binary row span of the incidence matrices of the designs. Further-more, we present a number of interesting ∆-divisible binary codes invariant under M11.