Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.781742 
Title:  On decompositions of finite projective planes and their applications  
Author:  Hazzazi, Mohammad Mazyad M. 
ISNI:
0000 0004 7967 3602


Awarding Body:  University of Sussex  
Current Institution:  University of Sussex  
Date of Award:  2019  
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Abstract:  
Let PG(2; q) be the projective plane over the field Fq. Singer [19] notes that PG(2; q) has a cyclic group of order q2 + q + 1 that permutes the points of PG(2; q) in a single cycle. A karc set of k points no three of which are collinear. A karc is called complete if it is not contained in a (k + 1)arc of PG(2; q). By taking the orbits of points under a proper subgroup of a single cycle, one can decompose the projective plane PG(2; qk) into disjoint copies of subplanes isomorphic to PG(2; q) if and only if k is not divisible by three. Moreover, by taking the orbits of points under a proper subgroup, one can decompose the projective plane PG(2; q2) into disjoint copies of complete (q2  q + 1)arcs. In this thesis, our main problem is to classify (up to isomorphism) the different types of decompositions of PG(2 ;q2) for q = 3; 4; 5; 7, namely subplanes and arcs. We further illustrate some of the connections between these subgeometry decompositions and other areas of combinatorial interest; in particular, we explain the relationship between coding theory and projective spaces and describe the links with Hermitian unital. Furthermore, projective codes are obtained by taking the disjoint union of such subgeometries.


Supervisor:  Not available  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.781742  DOI:  Not available  
Keywords:  QA0564 Algebraic geometry  
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