12 research outputs found

    Two Families of Blocking Semiovals

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    AbstractThe study of blocking semiovals in finite projective planes was motivated by Batten in connection with cryptography and was begun by Dover . In this note, two new families of blocking semiovals are constructed in desarguesian planes

    A survey on semiovals

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    A semioval in a finite projective plane is a non-empty pointset S with the property that for every point in SS there exists a unique line t_P such that StP=PS \cap t_P = {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 cryptography (determining sets). We survey the results on semiovals and give some new proofs

    A survey on semiovals

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    Some Blocking Semiovals which Admit a Homology Group

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    AbstractThe study of blocking semiovals in finite projective planes was motivated by Batten in connection with cryptography. Dover in studied blocking semiovals in a finite projective plane of order q which meet some line inq− 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. Any blocking semioval in the first or the third family meets no line in q− 1 points

    Blocking semiovals of Type (1,M+1,N+1)

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    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 \leq m < n. For those prime powers q1024q \leq 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+1 is a prime or three times a prime, then only the same trivial example can exist in a projective plane of order q. <br /

    2-semiarcs in PG(2, q), q <= 13

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    A 2-semiarc is a pointset S-2 with the property that the number of tangent lines to S-2 at each of its points is two. Using some theoretical results and computer aided search, the complete classification of 2-semiarcs in PG(2, q) is given for q <= 7, the spectrum of their sizes is determined for q <= 9, and some results about the existence are proven for q = 11 and q = 13. For several sizes of 2-semiarcs in PG(2, q), q <= 7, classification results have been obtained by theoretical proofs

    Finite Geometry Conference and Workshop 2013 június 10-14.

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