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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Codes Related to and Derived from Hamming Graphs

Muthivhi, Thifhelimbilu Ronald January 2013 (has links)
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.
2

Codes Related to and Derived from Hamming Graphs

Muthivhi, Thifhelimbilu Ronald January 2013 (has links)
>Magister Scientiae - MSc / For integers n, k 2:: 1, and k ~ n, the graph r~has vertices the 2n vectors of lF2 and adjacency defined by two vectors being adjacent if they differ in k coordinate positions. In particular, r~is the classical n-cube, usually denoted by Hl (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 first 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 Hl(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.

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