Doctor of Philosophy in Applied Mathematics
|Vincent Nyongesa Marani||PhD/MAT/003/2014||Modular Representation Of The Mathieu Groups As Linear Codes|
Given a permutation group G on a finite set and a field F it is our interest to know the structure of the permutation module .The G-invariant submodules of are regarded as linear codes in and we are interested in the weight distribution of these codes. We shall attempt to construct and enumerate all binary linear codes from modular representation of Mathieu simple groups by use of computer programs in Magma to search for irreducible modules. We shall also determine the properties of these codes and Interplay these codes with some designs, graphs and finite geometries. Many classes of codes have practical applications. It is hoped that knowledge from codes constructed from Mathieu will be used for error detection and error correction in communication and storage channels.