Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.554592 |
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Title: | The geometry of the plan of order seventeen and its application to error-correcting codes | ||||||
Author: | Al-Seraji, Najm Abdulzahra Makhrib |
ISNI:
0000 0004 2724 0581
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Awarding Body: | University of Sussex | ||||||
Current Institution: | University of Sussex | ||||||
Date of Award: | 2010 | ||||||
Availability of Full Text: |
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Abstract: | |||||||
The aim of the thesis is to classify certain geometric structures, called arcs, in a particular setting, namely the projective plane of order seventeen. The main computing tool is the mathematical programming language GAP. First, subsets of the line PG(1; 17) are classiffied. The results on the line PG(1; 17) classify sets of points on the conic on PG(2; 17), since there is a one-to-one correspondence between a set of points on PG(1; 17) and a set of the same size on a conic in PG(2; 17). In the plane PG(2; 17) the important arcs are called complete and are those that cannot be increased to a larger arc. So far, all arcs up to and including size eight have been classiffied, as have complete 10-arcs, 11-arcs, 12-arcs, 13-arcs and 14-arcs. In the plane of order seventeen, the maximum size is eighteen. Each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length. Cubic curves and the related (k; 3)-arcs in PG(2; 17) are also considered. A classiffication of both complete and incomplete curves is determined.
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Supervisor: | Not available | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.554592 | DOI: | Not available | ||||
Keywords: | QA Mathematics | ||||||
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