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Type: Journal article
Title: Characterising pointsets in PG(4,q) that correspond to conics
Author: Barwick, S.
Jackson, W.
Citation: Designs, Codes, and Cryptography, 2015; 80(2):317-332
Publisher: Springer
Issue Date: 2015
ISSN: 0925-1022
Statement of
S. G. Barwick, Wen-Ai Jackson
Abstract: We consider a non-degenerate conic in PG(2,q2), q odd, that is tangent to ℓ∞ and look at its structure in the Bruck–Bose representation in PG(4,q). We determine which combinatorial properties of this set of points in PG(4,q) are needed to reconstruct the conic in PG(2,q2). That is, we define a set C in PG(4,q) with q2 points that satisfies certain combinatorial properties. We then show that if q≥7, we can use C to construct a regular spread S in the hyperplane at infinity of PG(4,q), and that C corresponds to a conic in the Desarguesian plane P(S)≅PG(2,q2) constructed via the Bruck–Bose correspondence.
Description: Received: 23 November 2014 / Revised: 8 April 2015 / Accepted: 1 May 2015 / Published online: 20 May 2015
Rights: © Springer Science+Business Media New York 2015
RMID: 0030030077
DOI: 10.1007/s10623-015-0093-3
Appears in Collections:Mathematical Sciences publications

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