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 in the nineteen thirty's. The second method is a generalization 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 arc two recent techniques developed by J .D. Key and J. Moori (2002). they use primitive finite groups to build l-designs. We will apply these methods to simple groups, and use the incidence matrix of the constructed designs to generate codes.