Codes, graphs and designs from maximal subgroups of alternating groups

• Main Author: Mumba, Nephtale Bvalamanja
• Other Authors: Mwambene, Eric
• Language: en
• Published: University of the Western Cape 2018
• Subjects: Alternating groups; Automorphism groups; Antipodal graphs; Bipartite graphs; Designs; Graphs; Graph covers; Incidence design; Linear code; Maximal subgroups; Neighbourhood design; Permutation decoding
• Online Access: http://hdl.handle.net/11394/6165

Philosophiae Doctor - PhD (Mathematics) === The main theme of this thesis is the construction of linear codes from adjacency matrices or sub-matrices of adjacency matrices of regular graphs. We first examine the binary codes from the row span of biadjacency matrices and their transposes for some classes of bipartite graphs. In this case we consider a sub-matrix of an adjacency matrix of a graph as the generator of the code. We then shift our attention to uniform subset graphs by exploring the automorphism groups of graph covers and some classes of uniform subset graphs. In the sequel, we explore equal codes from adjacency matrices of non-isomorphic uniform subset graphs and finally consider codes generated by an adjacency matrix formed by adding adjacency matrices of two classes of uniform subset graphs.