The André/Bruck and Bose representation of conics in Baer subplanes of PG(2,q 2)

2002 ◽  
Vol 74 (1) ◽  
pp. 123-138 ◽  
Author(s):  
Catherine T. Quinn
Keyword(s):  
Baer Subplanes

Baer Subplanes, Ovals and Unitals

1990 ◽  
pp. 1-8 ◽  
Author(s):  
E. F. Assmus ◽  
J. D. Key
Keyword(s):  
Baer Subplanes

Relative blocking sets of unions of Baer subplanes

2018 ◽  
Vol 87 (4) ◽  
pp. 865-877
Author(s):  
Aart Blokhuis ◽  
Leo Storme ◽  
Tamás Szőnyi
Keyword(s):  
Blocking Sets ◽  
Baer Subplanes

Lacunary Polynomials, Multiple Blocking Sets and Baer Subplanes

1999 ◽  
Vol 60 (2) ◽  
pp. 321-332 ◽  
Author(s):  
A. Blokhuis ◽  
L. Storme ◽  
T. Szőnyi
Keyword(s):  
Blocking Sets ◽  
Baer Subplanes

A formal analogy between Baer subplanes and their complements

1975 ◽  
Vol 6 (2) ◽  
pp. 97-104
Author(s):  
T. A. McKee
Keyword(s):  
Baer Subplanes ◽  
Formal Analogy

scholarly journals Baer subplanes of projective planes.

1975 ◽  
Author(s):  
Rilla Nichols
Keyword(s):  
Projective Planes ◽  
Baer Subplanes

scholarly journals Blocking and Double Blocking Sets in Finite Planes

10.37236/5717 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Jan De Beule ◽  
Tamás Héger ◽  
Tamás Szőnyi ◽  
Geertrui Van de Voorde
Keyword(s):  
Projective Planes ◽  
Blocking Set ◽  
Blocking Sets ◽  
Desarguesian Plane ◽  
Baer Subplanes ◽  
Desarguesian Projective Planes ◽  
Finite Planes ◽  
Value Sets ◽  
Minimal Blocking ◽  
Desarguesian Affine Plane

In this paper, by using properties of Baer subplanes, we describe the construction of a minimal blocking set in the Hall plane of order $q^2$ of size $q^2+2q+2$ admitting $1-$, $2-$, $3-$, $4-$, $(q+1)-$ and $(q+2)-$secants. As a corollary, we obtain the existence of a minimal blocking set of a non-Desarguesian affine plane of order $q^2$ of size at most $4q^2/3+5q/3$, which is considerably smaller than $2q^2-1$, the Jamison bound for the size of a minimal blocking set in an affine Desarguesian plane of order $q^2$.We also consider particular André planes of order $q$, where $q$ is a power of the prime $p$, and give a construction of a small minimal blocking set which admits a secant line not meeting the blocking set in $1$ mod $p$ points. Furthermore, we elaborate on the connection of this problem with the study of value sets of certain polynomials and with the construction of small double blocking sets in Desarguesian projective planes; in both topics we provide some new results.

On transitive Baer subplanes of generalized Hall planes

1980 ◽  
Vol 9 (3) ◽  
Author(s):  
C.A.M. Klever
Keyword(s):  
Baer Subplanes

Unitals which meet Baer subplanes in 1 moduloq points

2000 ◽  
Vol 68 (1-2) ◽  
pp. 16-22 ◽  
Author(s):  
S. G. Barwick ◽  
Christine M. O'Keefe ◽  
L. Storme
Keyword(s):  
Baer Subplanes

A class of doubly resolvable GDDs from Baer subplanes

2001 ◽  
Vol 94 (2) ◽  
pp. 421-427
Author(s):  
L. Zhu
Keyword(s):  
Baer Subplanes ◽  
Doubly Resolvable

scholarly journals On multiple blocking sets in Galois planes

2007 ◽  
Vol 7 (1) ◽  
pp. 39-53 ◽  
Author(s):  
A Blokhuis ◽  
L Lovász ◽  
L Storme ◽  
T Szőnyi
Keyword(s):  
Pairwise Disjoint ◽  
London Math ◽  
Algebraic Curves ◽  
Blocking Sets ◽  
Baer Subplane ◽  
Baer Subplanes ◽  
Galois Planes

AbstractThis article continues the study of multiple blocking sets in PG(2,q). In [A. Blokhuis, L. Storme, T. Szőnyi, Lacunary polynomials, multiple blocking sets and Baer subplanes.J. London Math. Soc. (2)60(1999), 321–332. MR1724814 (2000j:05025) Zbl 0940.51007], using lacunary polynomials, it was proven thatt-fold blocking sets of PG(2,q),qsquare,t<q¼/2, of size smaller thant(q+ 1) +cqq⅔, withcq= 2−⅓whenqis a power of 2 or 3 andcq= 1 otherwise, contain the union oftpairwise disjoint Baer subplanes whent≥ 2, or a line or a Baer subplane whent= 1. We now combine the method of lacunary polynomials with the use of algebraic curves to improve the known characterization results on multiple blocking sets and to prove at(modp) result on smallt-fold blocking sets of PG(2,q=pn),pprime,n≥ 1.

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