Designs and binary codes from maximal subgroups and conjugacy classes of ({rm M}_{11})

By using a method of construction of block-primitive and point-transitive 1-designs, in this paper we determine all block-primitive and point-transitive 1-((v, k, lambda))-designs from the maximal subgroups and the conjugacy classes of elements of the small Mathieu group ({rm M}_{11}). We examine the properties of the 1-((v, k, lambda))-designs and construct the codes defined by the binary row span of their incidence matrices. Furthermore, we present a number of interesting (Delta)-divisible binary codes invariant under ({rm M}_{11})

Designs and binary codes from maximal subgroups and conjugacy classes of the Mathieu group M11

Please read abstract in the article.The National Research Foundation of South Africahttp://www.mathos.hr/mcam2022Mathematics and Applied Mathematic