Designs and codes from fixed points of elements of Janko simple group J₁

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 $J_1,$ for the first 3 conjugacy classes of maximal subgroups and its 2A, 3A, 5A and 7A conjugacy classes of elements.

Keywords:

• Designs
• codes
• simple groups
• sporadic groups
• Janko group
• fixed points
• maximal subgroups
• conjugacy classes

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D05
• 20D08
• 94B60

Acknowledgments

The author acknowledges supports from NWU (Mafikeng) and would like to thank the School of Mathematics at the University of Birmingham (UK).