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Discrete Mathematics
Volume 294, Issues 1-2, 28 April 2005, Pages 5-11
Finite Geometries
 
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doi:10.1016/j.disc.2004.04.031    
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Copyright © 2005 Elsevier B.V. All rights reserved.

Maximal arc partitions of designs

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A.N. Al-Kenania, E-mail The Corresponding Author and V.C. Mavronb, E-mail The Corresponding Author

aDepartment of Mathematics, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia

bDepartment of Mathematics, The University of Wales, Penglais, Aberystwyth, Ceredigion, Wales SY23 3BZ, UK


Received 30 April 2003; 
revised 23 October 2003; 
accepted 29 April 2004. 
Available online 3 March 2005.

Abstract

It is known that the designs PGn-1(n,q) in some cases have spreads of maximal α-arcs. Here a α-arc is a non-empty subset of points that meets every hyperplane in 0 or α points. The situation for designs in general is not so well known. This paper establishes an equivalence between the existence of a spread of α-arcs in the complement of a Hadamard design and the existence of an affine design and a symmetric design which is also the complement of a Hadamard design.

Keywords: Design; Hadamard 2-design; Arc

MSC: 51E05

Article Outline

1. Introduction
2. Basic results and definitions
3. Spreads and α-arcs
References

Discrete Mathematics
Volume 294, Issues 1-2, 28 April 2005, Pages 5-11
Finite Geometries
 
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