Designs and binary codes from maximal subgroups and conjugacy classes of ${\rm M}_{11}$
Gareth Amery, Stuart Gomani, Bernardo Gabriel Rodrigues · Hrčak Portal of scientific journals of Croatia (University Computing Centre) · 2021
By using a method of constructing block-primitive and point-transitive 1designs, 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.Furthermore, we present a number of interesting ∆-divisible binary codes invariant under M11.