Relative blocking sets of unions of Baer subplanes

Aart Blokhuis; Leo Storme; Tamás Szőnyi

doi:10.1007/s10623-018-0575-1

Relative blocking sets of unions of Baer subplanes

Aart Blokhuis, Leo Storme (Corresponding author), Tamás Szőnyi

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

Abstract

We show that, for small t, the smallest set that blocks the long secants of the union of t pairwise disjoint Baer subplanes in PG (2 , q²) has size t(q+ 1) and consists of t Baer sublines, and, for large t, the smallest such set has size q²+ q+ 1 and is itself a Baer subplane of PG (2 , q²). We also present a stability result in the first case.

Original language	English
Pages (from-to)	865-877
Number of pages	13
Journal	Designs, Codes and Cryptography
Volume	87
Issue number	4
Early online date	28 Oct 2018
DOIs	https://doi.org/10.1007/s10623-018-0575-1
Publication status	Published - 15 Apr 2019

Keywords

Baer subplanes
Blocking sets
Fractional cover
Fractional covering number
Relative blocking sets

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10.1007/s10623-018-0575-1

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AU - Szőnyi, Tamás

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N2 - We show that, for small t, the smallest set that blocks the long secants of the union of t pairwise disjoint Baer subplanes in PG (2 , q2) has size t(q+ 1) and consists of t Baer sublines, and, for large t, the smallest such set has size q2+ q+ 1 and is itself a Baer subplane of PG (2 , q2). We also present a stability result in the first case.

AB - We show that, for small t, the smallest set that blocks the long secants of the union of t pairwise disjoint Baer subplanes in PG (2 , q2) has size t(q+ 1) and consists of t Baer sublines, and, for large t, the smallest such set has size q2+ q+ 1 and is itself a Baer subplane of PG (2 , q2). We also present a stability result in the first case.

KW - Baer subplanes

KW - Blocking sets

KW - Fractional cover

KW - Fractional covering number

KW - Relative blocking sets

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JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

IS - 4

ER -

Relative blocking sets of unions of Baer subplanes

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