Some p-ranks related to orthogonal spaces

A. Blokhuis; G.E. Moorhouse

doi:10.1023/A:1022477715988

Some p-ranks related to orthogonal spaces

A. Blokhuis, G.E. Moorhouse

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-review

61 Citations (Scopus)

Abstract

We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p e) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in O10+ (2e ),O10+ (3e ),O9 (5e ),O12+ (5e )O+10(2e)O+10(3e)O9(5e)O+12(5e) and O12+ (7e )O+12(7e) . We also give slightly weaker bounds for more general finite classical polar spaces. Another application is the determination of certain explicit bases for the code of PG(2, p) using secants, or tangents and passants, of a nondegenerate conic.

Original language	English
Pages (from-to)	295-316
Number of pages	22
Journal	Journal of Algebraic Combinatorics
Volume	4
Issue number	4
DOIs	https://doi.org/10.1023/A:1022477715988
Publication status	Published - 1995

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abstract = "We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p e) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in O10+ (2e ),O10+ (3e ),O9 (5e ),O12+ (5e )O+10(2e)O+10(3e)O9(5e)O+12(5e) and O12+ (7e )O+12(7e) . We also give slightly weaker bounds for more general finite classical polar spaces. Another application is the determination of certain explicit bases for the code of PG(2, p) using secants, or tangents and passants, of a nondegenerate conic.",

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JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 4

ER -

Some p-ranks related to orthogonal spaces

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