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Blocking Sets of Almost Rédei Type

✍ Scribed by A. Blokhuis; R. Pellikaan; Tamás Szőnyi

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
312 KB
Volume
78
Category
Article
ISSN
0097-3165

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✦ Synopsis

We study minimal blocking sets in PG(2, q) having q+m points outside some fixed line. If 0<m<(-q)Â2 then either the blocking set is large, or every line contains 1 mod p points of the blocking set, where p is the characteristic of the field GF(q). 1997 Academic Press 1. INTRODUCTION A blocking set in a projective plane is a set B of points, such that every line contains at least one point of B. If B contains a line, it is called trivial. If no proper subset of B is a blocking set it is called minimal. Let B be a non-trivial minimal blocking set, and let L be a line containing l<q+1 points of B. Then it follows immediately that |B| q+l, by considering the lines through a point P of L not belonging to the blocking set. If we have equality, then every line through P different from L contains precisely one point of B. Blocking sets of this kind are called of Re dei type and were studied in [7, 5]. If q= p h , p prime, and l<(q+1)Â2, then it follows from Re dei's results [13, Section 36] that each line intersects the blocking set in 1 (mod p) points. Moreover, from his results we get that for a non-trivial blocking set B of Re dei-type either |B| q+(q+1)Â2, or q+1+(q&1)Â ( p e +1) |B| q+(q&1)Â( p e &1) for some e, 1 e [nÂ2]. His result article no. TA962736 141 0097-3165Â97 25.00

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