Designs and codes from fixed points of elements of Janko simple group J 1

Abstract

We previously have developed two methods for constructing codes and designs from finite groups (mostly simple finite groups). In a recent paper we introduced a new method (Method 3) for constructing codes and designs from fixed points of elements of finite transitive groups. This new method together with background material and results required from finite groups, permutation groups and representation theory were discussed fully in that paper. The main aim of this paper is to apply the method to the first Janko sporadic simple group for the first 3 conjugacy classes of maximal subgroups and its 2A, 3A, 5A and 7A conjugacy classes of elements.