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Title: Classification of arcs in galois plane of order thirteen
Author: Ali, Abbas Husain
Awarding Body: University of Sussex
Current Institution: University of Sussex
Date of Award: 1993
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The main theme of this thesis is to classify subsets in PG(2, 13) of k elements where no three are collinear. Such sets are called k-arcs. In particular, we are interested in the values of k for which the k-arc is complete. Chapter 1 is devoted to basic definitions of projective spaces of n dimensions, subspaces and the fundamental theorem of projective geometry. Chapter 2 is a preliminary to the main task. It contains the construction of PG(1, q) and the classification of all subsets of PG(1, 13). Chapter 3 is devoted to the construction of PG(2, q), derivation of some general equations and a few small results used in the plane. Chapter 4 is the main one and it contains the complete classification of k-arcs in PG(2, 13). In Chapter 5 the work is extended to projective spaces of order 17 and 19 as a test for the computer programs. Finally, there is a list of the programs used as well as tables of the points of the planes discussed throughout the work.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available