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dc.contributor.advisorMwambene, E.C.
dc.contributor.authorMuthivhi, Thifhelimbilu Ronald
dc.date.accessioned2015-04-30T13:03:17Z
dc.date.available2015-04-30T13:03:17Z
dc.date.issued2013
dc.identifier.urihttp://hdl.handle.net/11394/4091
dc.descriptionMasters of Scienceen_US
dc.description.abstractCodes Related to and Derived from Hamming Graphs T.R Muthivhi M.Sc thesis, Department of Mathematics, University of Western Cape For integers n; k 1; and k n; the graph 􀀀k n has vertices the 2n vectors of Fn2 and adjacency de ned by two vectors being adjacent if they di er in k coordinate positions. In particular, 􀀀1 n is the classical n-cube, usually denoted by H1(n; 2): This study examines the codes (both binary and p-ary for p an odd prime) of the row span of adjacency and incidence matrices of these graphs. We rst examine codes of the adjacency matrices of the n-cube. These have been considered in [14]. We then consider codes generated by both incidence and adjacency matrices of the Hamming graphs H1(n; 3) [12]. We will also consider codes of the line graphs of the n-cube as in [13]. Further, the automorphism groups of the codes, designs and graphs will be examined, highlighting where there is an interplay. Where possible, suitable permutation decoding sets will be given.en_US
dc.language.isoenen_US
dc.publisherUniversity of the Western Capeen_US
dc.subjectAutomorphism Cayley graphs Codes Cubes Designs Dual codes Hamming graphs Permutation decoding Ternary codes Vertex-transitivityen_US
dc.titleCodes Related to and Derived from Hamming Graphsen_US
dc.rights.holderUniversity of the Western Capeen_US


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