Designs and codes from involutions of A_n

Abstract

We previously have developed two methods for constructing codes and designs from finite simple 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 fixed points of involutions of the Alternating group A_n (for n ≥ 5) on its action on Ω, 2-subsets (or duads) Γ^{2} of a set Γ of size n.

Mathematics Subject Classification (2020):

• Primary: 20D05
• 20D06
• 05B05
• Secondary: 94B60

Key words:

• Designs
• codes
• simple groups
• alternating groups
• fixed points
• maximal subgroups
• conjugacy classes