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Annals of Combinatorics On Generalized k-Arcs in PG(2n; q)

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Bibliographic Details
Title: Annals of Combinatorics On Generalized k-Arcs in PG(2n; q)
Authors: B. N. Cooperstein, J. A. Thas
Contributors: The Pennsylvania State University CiteSeerX Archives
Source: http://www.combinatorics.net/aoc/toc/v5n2/coop/5_2_141.pdf.
Publication Year: 1999
Collection: CiteSeerX
Subject Terms: projective space, k-arc, oval, hyperoval, strongly regular graph, partial geometry, two- weight code References
Description: AMS Subject Classication: 51E20, 05B25, 51E14, 94B27 Abstract. The notion of a generalized k-arc in PG(2n; q) is introduced. When k = q n+11 q1 + 1 it is demonstrated that the existence of a generalized k-arc in PG(2n; q) leads to a construction of a partial geometry, a strongly regular graph and a two-weight code. Such k-arcs are called generalized hyperovals. It is proved that no such generalized hyperovals exist when q is odd. For each n 2 and q = 2 it is shown that each generalized hyperoval of PG(2n; 2) is a partition of PG(2n; 2)nPG(n; 2): Related structures are also discussed.
Document Type: text
File Description: application/pdf
Language: English
Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.514.7025; http://www.combinatorics.net/aoc/toc/v5n2/coop/5_2_141.pdf
Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.514.7025
http://www.combinatorics.net/aoc/toc/v5n2/coop/5_2_141.pdf
Rights: Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Accession Number: edsbas.5C90194
Database: BASE
Description
Abstract:AMS Subject Classication: 51E20, 05B25, 51E14, 94B27 Abstract. The notion of a generalized k-arc in PG(2n; q) is introduced. When k = q n+11 q1 + 1 it is demonstrated that the existence of a generalized k-arc in PG(2n; q) leads to a construction of a partial geometry, a strongly regular graph and a two-weight code. Such k-arcs are called generalized hyperovals. It is proved that no such generalized hyperovals exist when q is odd. For each n 2 and q = 2 it is shown that each generalized hyperoval of PG(2n; 2) is a partition of PG(2n; 2)nPG(n; 2): Related structures are also discussed.