Waugh,_Karl_Michael_Vincent.pdf (1018.54 kB)
Partitions of codes
thesis
posted on 2023-06-08, 15:11 authored by Karl Michael Vincent WaughIn this thesis we look at coding theory wherein we introduce the concept of perspective, a generalisation on the minimum distance of a code, which naturally leads to a partition of the code. Subsequently we introduce focused splittings, which shall be shown to be a generalisation of perfect codes. We investigate the existence of such objects, and address questions such as the complexity of finding a focused splittings, which we show to be NPComplete. We analyse the symmetries of focused splittings. We use focused splittings to address the problem of error correction and we construct an encoding method based on them. Finally we test this construction for various classes of focused splittings.
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- Published version
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167.0Department affiliated with
- Mathematics Theses
Qualification level
- doctoral
Qualification name
- phd
Language
- eng
Institution
University of SussexFull text available
- Yes
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2013-06-06Usage metrics
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