Masters of Science / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uwc/oai:etd.uwc.ac.za:11394/4091 |
| Date | January 2013 |
| Creators | Muthivhi, Thifhelimbilu Ronald |
| Contributors | Mwambene, E.C. |
| Publisher | University of the Western Cape |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Rights | University of the Western Cape |
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