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• W2102452642 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 UBBs for groups which are base-transitive, i.e. which act transitively on their irredundant bases, which were classified by T. Maund. Various combinatorial, algebraic and number-theoretic techniques are employed in this. Other topics include a case study of the Mathieu group M12, where we investigate ways in which we can improve the performance of our algorithm, and how the group behaves as a code when number of errors received exceeds the correction capability. We also develop an alternative algorithm which works for the group Cm oSn, and compare its complexity with the original. There is also a chapter about what can be said for more general permutation groups when regarded as codes in this manner, where we formulate a conjecture (the “single orbit conjecture”) about UBBs for permutation groups in general, which we prove for some special cases." @default.
• W2102452642 created "2016-06-24" @default.
• W2102452642 creator A5047463270 @default.
• W2102452642 date "2005-01-01" @default.
• W2102452642 modified "2023-09-27" @default.
• W2102452642 title "Permutation Groups, Error-Correcting Codes and Uncoverings" @default.
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