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Permutation Groups, Error-Correcting Codes

Summary: Permutation Groups,
Error-Correcting Codes
and Uncoverings
Robert Francis Bailey
Queen Mary, University of London
Thesis submitted to the University of London for the degree of
Doctor of Philosophy
2nd November 2005
We replace the traditional setting for error-correcting codes (i.e. linear codes) with
that of permutation groups, with permutations in list form as the codewords. We
introduce a decoding algorithm for these codes, which uses the following notion.
A base for a permutation group is a sequence of points whose stabiliser is trivial.
An uncovering-by-bases (or UBB) is a set of bases such that any combination of
error positions is avoided by at least one base in the set. In the case of sharply
k-transitive groups, any k-tuple of points forms a base, so a UBB can be formed
from the complements of the blocks of a covering design. (In this case, we use the
term uncovering.)
A large part of the thesis (chapters 2 to 5) is concerned with constructing


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics