dc.contributor.advisor | Mwambene, E.C. | |
dc.contributor.author | Muthivhi, Thifhelimbilu Ronald | |
dc.date.accessioned | 2015-04-30T13:03:17Z | |
dc.date.available | 2015-04-30T13:03:17Z | |
dc.date.issued | 2013 | |
dc.identifier.uri | http://hdl.handle.net/11394/4091 | |
dc.description | Masters of Science | en_US |
dc.description.abstract | Codes 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.iso | en | en_US |
dc.publisher | University of the Western Cape | en_US |
dc.subject | Automorphism Cayley graphs Codes Cubes Designs Dual codes Hamming graphs Permutation decoding Ternary codes Vertex-transitivity | en_US |
dc.title | Codes Related to and Derived from Hamming Graphs | en_US |
dc.rights.holder | University of the Western Cape | en_US |