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Rédei Blocking Sets in Finite Desarguesian Planes
2002
Journal of combinatorial theory. Series A
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PRELIMINARIES A blocking set in a projective plane is a set of points of the plane which contains at least one point of each line, but not all the points of any of them. ...
Sherman [7] has characterised Rédei blocking sets with at least two Rédei lines in terms of additive and multiplicative groups of GF(q). ...
projective plane of order q which meets at least one line in exactly n points-and Bruen and Silverman [2] renamed this concept a blocking set of Rédei type. ...
doi:10.1006/jcta.2001.3242
fatcat:34ugzhcapbepzkfkbnqsnembya
Page 5622 of Mathematical Reviews Vol. , Issue 2001H
[page]
2001
Mathematical Reviews
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The blocking sets of Rédei type in PG(2, p*) have size p> + p? + 1 or p> + p? + p+, as was proved by the author earlier. For g = p, p prime, there are no small blocking sets [A. ...
The very nice paper under review shows that all small minimal blocking sets in PG(2,q), gq = p*, p prime, p >7, are of Rédei type. ...
Page 5593 of Mathematical Reviews Vol. , Issue 97I
[page]
1997
Mathematical Reviews
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A connection of U with an inversive plane, known in the case where I is Desarguesian, is extended to the non- Desarguesian case. ...
A blocking set B is a set of points intersecting every line but not containing a line. It is said to be of Rédei type if there is a line intersecting it in exactly |B| - q points. ...
Page 7387 of Mathematical Reviews Vol. , Issue 2002J
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2002
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When every line meets a blocking set B in | modulo gq points then B is either a Baer subplane (which exists only when q is a square) or B is of Rédei type. ...
Codes Cryptogr. 20 (2000), no. 3, 319-324; MR 2001h:51018] proved that minimal blocking sets of size less than 3(g + 1)/2 are of Rédei type when g = p’. ...
Page 6903 of Mathematical Reviews Vol. , Issue 2003i
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2003
Mathematical Reviews
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In a Rédei blocking set, a subset of / collinear points is called a Rédei line.
In this paper, Rédei blocking sets with at least two Rédei lines and 3 <h <gq-—1 are examined. ...
is called a Rédei blocking set. ...
Page 4037 of Mathematical Reviews Vol. , Issue 2001F
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2001
Mathematical Reviews
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In the Desarguesian plane PG(2, q‘) one can construct a blocking set of Rédei type, having q‘ + q‘~'+1 points, starting from the graph of the trace function from GF(q‘) to GF(q) [see A. ...
B is called a blocking set of Rédei type, if there is a line / for which |BN/| =|B|— q. In this case the line / is called a Rédei line for B. ...
Page 3586 of Mathematical Reviews Vol. , Issue 2003e
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2003
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2003e:5 1015
sizes of small minimal blocking sets: the Rédei type GF(q)-linear blocking sets must have size g? + q°>+1 and g++q°+q? ...
+cq+1, c € {—1,0,1}, while the non-Rédei type blocking sets must have size gi + q3+q°?+dq+1, with d € {0,1}. It is also shown that each possible cardinality actually occurs. ...
Direction problems in affine spaces
[article]
2014
arXiv
pre-print
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This paper is a survey paper on old and recent results on direction problems in finite dimensional affine spaces over a finite field. ...
More information on blocking sets of Desarguesian projective planes can be found in [17] . The situation for non-Desarguesian planes is more complicated, especially the construction of examples. ...
Apart from [18] and [19] , the papers [10, 11, 30] are interesting references for blocking sets of non Desarguesian planes. ...
arXiv:1409.6960v1
fatcat:5x4wlbtqifh7re3mhhmrwdfl5e
Page 5039 of Mathematical Reviews Vol. , Issue 2002G
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2002
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Linear blocking sets pro- vided the first examples of small minimal blocking sets which are not of Rédei type. ...
In the nice paper under review the authors show that a GF(q)- linear blocking set of Rédei type defines a derivable partial spread in PG(2t —1,q). ...
Page 3260 of Mathematical Reviews Vol. , Issue 99e
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1999
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A blocking set is said to be of Rédei type if there is a line / such that |@ \/| = q; these are extremal in the sense that for any blocking set # and line / in z we have |#~/| > q. ...
In this case / is called the Rédei line. Further, a blocking set @ in PG(2, p) is said to be of almost Rédei type if there is a line / such that |A \/| € {p,p+1,p+2}. ...
Page 1253 of Mathematical Reviews Vol. , Issue 2000b
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2000
Mathematical Reviews
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The authors construct small minimal blocking sets not of Rédei type in an infinite family of non-Desarguesian translation planes, namely, André planes constructed from spreads in projective spaces. ...
A (nontrivial) blocking set in a projective plane I is a set @ of points such that every line meets (but is not contained in) #. & is minimal if no proper subset is a blocking set. ...
Page 6198 of Mathematical Reviews Vol. , Issue 97J
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1997
Mathematical Reviews
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There is only one known minimal blocking set B in PG(2, p) that is not of Rédei type. ...
satisfies p <7 and all such blocking sets are of Rédei type (relative to a line #/) apart from the exceptional example in PG(2,7) indicated above. ...
Page 1370 of Mathematical Reviews Vol. , Issue 87c
[page]
1987
Mathematical Reviews
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The methods in both papers are nonconstructive. S. Stein (Davis, Calif.)
87c:51012
Blokhuis, A. (NL-EIND);
Brouwer, A. E. (NL-MATH)
Blocking sets in Desarguesian projective planes.
Bull. London Math. ...
A blocking set in a projective plane P of order q is a set B of points such that any line contains a point of B and a point off B. It is well known [A. A. Bruen, SIAM J. Appl. ...
Blocking sets and semifields
2006
Journal of combinatorial theory. Series A
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We find a relationship between semifield spreads of PG(3, q), small Rédei minimal blocking sets of PG(2, q 2 ), disjoint from a Baer subline of a Rédei line, and translation ovoids of the hermitian surface ...
I gratefully acknowledge the referee for having pointed out that in [17] Johnson has proved that a transversal of a derivable net produces an indicator set, and therefore transversal functions and indicator ...
sets are equivalent; hence, the results and the techniques of [17] might be used to provide an answer to some of the problems posed here. ...
doi:10.1016/j.jcta.2005.11.001
fatcat:yl4aoqf47jbtjloifhabd3kmmm
Page 1471 of Mathematical Reviews Vol. , Issue 92c
[page]
1992
Mathematical Reviews
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A blocking set in a projective plane is a set B of points such that any line has a point in B as well as a point outside B. If the projective plane has order n = m? ...
Kallaher (1-WAS)
92¢:51015 51E21 05B25
Drake, David A. (1-FL)
A bound for blocking sets in finite projective planes.
Finite geometries and combinatorial designs (Lincoln, NE, 1987), 93-97, Contemp. ...
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