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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
2
Abstract
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
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