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- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Kluwer Academic Publishers
- Subject
- Mathematics; Computer Science, general; Group Theory and Generalizations; Order, Lattices, Ordered Algebraic Structures; Combinatorics; Convex and Discrete Geometry
- ISSN
- 0925-9899
- eISSN
- 1572-9192
- DOI
- 10.1023/B:JACO.0000022564.51008.63
- Publisher site
- See Article on Publisher Site
Abstract
A d-dimensional dual arc in PG(n, q) is a higher dimensional analogue of a dual arc in a projective plane. For every prime power q other than 2, the existence of a d-dimensional dual arc (d ≥ 2) in PG(n, q) of a certain size implies n ≤ d(d + 3)/2 (Theorem 1). This is best possible, because of the recent construction of d-dimensional dual arcs in PG(d(d + 3)/2, q) of size ∑ d−1 i=0 q i, using the Veronesean, observed first by Thas and van Maldeghem (Proposition 7). Another construction using caps is given as well (Proposition 10).
Journal
Journal of Algebraic Combinatorics – Springer Journals
Published: Sep 30, 2004