منابع مشابه
Small Complete Arcs in Projective Planes
In the late 1950’s, B. Segre introduced the fundamental notion of arcs and complete arcs [48, 49]. An arc in a finite projective plane is a set of points with no three on a line and it is complete if cannot be extended without violating this property. Given a projective plane P, determining n(P), the size of its smallest complete arc, has been a major open question in finite geometry for severa...
متن کاملOn small complete arcs in a finite plane
Recent results on blocking sets are applied to the bisecants of a small complete arc, since these lines form a dual blocking set. It is shown that such blocking sets yield a lacunary polynomial of specific type. This leads to an improvement to the lower bound of the existence of a complete k-arc when the order of the plane is a square prime.
متن کاملConstructions of small complete arcs with prescribed symmetry
We use arcs found by Storme and van Maldeghem in their classification of primitive arcs in PG(2, q) as seeds for constructing small complete arcs in these planes. Our complete arcs are obtained by taking the union of such a “seed arc” with some orbits of a subgroup of its stabilizer. Using this approach we construct five different complete 15arcs fixed by Z3 in PG(2, 37), a complete 20-arc fixe...
متن کاملComplete Arcs in Steiner Triple Systems
A complete arc in a design is a set of elements which contains no block, and is maximal with respect to this property. The spectrum of sizes of complete arcs in Steiner triple systems is determined without exception here.
متن کاملOn Complete Arcs Arising from Plane Curves
We point out an interplay between Fq-Frobenius non-classical plane curves and complete (k, d)-arcs in P2(Fq). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q − d + 2) and d = (q − 1)/(q − 1), q being a power of the characteristic. In addi...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 1999
ISSN: 1071-5797
DOI: 10.1006/ffta.1998.0229