منابع مشابه
Blocking Semiovals of Type
We consider the existence of blocking semiovals in finite projective planes which have intersection sizes 1,m+ 1 or n+ 1 with the lines of the plane for 1 ≤ m < n. For those prime powers q ≤ 1024, in almost all cases, we are able to show that, apart from a trivial example, no such blocking semioval exists in a projective plane of order q. We are also able to prove, for general q, that if q2 + q...
متن کاملSome new results on small blocking semiovals
A blocking semioval S in a projective plane of order q is a set of points such that every line meets S in at least one point (the blocking property), and every point of S lies on a unique tangent line (the semioval property). The set of points on the sides of a triangle, excluding the vertices, is a blocking semioval in any projective plane of order q > 2, and has size 3q − 3. The size of a blo...
متن کاملBlocking Semiovals of Type (1, m+1, n+1)
We consider the existence of blocking semiovals in nite projective planes which have intersection sizes 1; m + 1 or n + 1 with the lines of the plane, for 1 m < n. For those prime powers q 1024, in almost all cases, we are able to show that, apart from a trivial example, no such blocking semioval exists in a projective plane of order q. We are able to prove also, for general q, that if q 2 + q ...
متن کاملSome Blocking Semiovals which Admit a Homology Group
The study of blocking semiovals in finite projective planes was motivated by Batten [1] in connection with cryptography. Dover in [4] studied blocking semiovals in a finite projective plane of order q which meet some line in q − 1 points. In this note, some blocking semiovals in PG(2, q) are considered which admit a homology group, and three new families of blocking semiovals are constructed. A...
متن کاملA survey on semiovals
A semioval in a finite projective plane is a non-empty pointset S with the property that for every point in S there exists a unique line tP such that S ∩ tP = {P}. This line is called the tangent to S at P . Semiovals arise in several parts of finite geometries: as absolute points of a polarity (ovals, unitals), as special minimal blocking sets (vertexless triangle), in connection with cryptogr...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2003
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(02)00147-6