✦ LIBER ✦

A Lower Bound on Blocking Semiovals

✍ Scribed by Jeremy M. Dover

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 87 KB
Volume: 21
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0371

No coin nor oath required. For personal study only.

✦ Synopsis

A semioval in a projective plane is a set S of points such that for every point P ∈ S, there exists a unique line of such that ∩ S = {P}. In other words, at every point of S, there exists a unique tangent line. A blocking set in is a set B of points such that every line of contains at least one point of B, but is not entirely contained in B. Combining these notions, we obtain the concept of a blocking semioval, a set of points in a projective plane which is both a semioval and a blocking set. Batten [1] indicated applications of such sets to cryptography, which motivates their study. In this paper, we give some lower bounds on the size of a blocking semioval, and discuss the sharpness of these bounds.

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