Some Blocking Semiovals which Admit a Homology Group

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

A 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 t_P such that $S \cap t_P = {P}$. 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