Designs and codes from certain finite simple groups

Abstract

In this dissertation , we study four methods for constructing codes and designs from finite groups. The first method was developed by Carmichael and Ernst Witt in the nineteen thirty's. The second method is a generalisation of the first one by D.R. Hughes in the nineteen sixty's. These first two methods use t-transitive groups to construct t-designs. The last methods are two recent techniques developed by J .D. Key and J .Moori (2002) , they use primitive finite groups to build 1-designs. We will apply these methods to simple groups, and use the incidence matrix of the constructed designs to generate codes.