Copyright © 2005 Elsevier B.V. All rights reserved.
Maximal arc partitions of designs
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






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