Search

In the history of secret sharing schemes many constructions are based on geometric objects. In this paper we investigate generalizations of threshold schemes and related finite geometric structures. In particular, we analyse compartmented and hierarchical schemes, and deduce some more general results, especially bounds for special arcs and novel constructions for conjunctive 2-level and 3-level hierarchical schemes. [ABSTRACT FROM AUTHOR]

In this paper, we show that a small minimal blocking set with exponent e in PG( n, p), p prime, spanning a ( t/ e − 1)-dimensional space, is an $${\mathbb{F}_{p^e}}$$ -linear set, provided that p > 5( t/ e)−11. As a corollary, we get that all small minimal blocking sets in PG( n, p), p prime, p > 5 t − 11, spanning a ( t − 1)-dimensional space, are $${\mathbb{F}_p}$$ -linear, hence confirming the linearity conjecture for blocking sets in this particular case. [ABSTRACT FROM AUTHOR]

In this article we prove a theorem about the number of directions determined by less then q affine points, similar to the result of Blokhuis et al. (in J. Comb. Theory Ser. A 86(1), 187-196, ) on the number of directions determined by q affine points. [ABSTRACT FROM AUTHOR]

The article pays tribute to the late mathematician András Gács who died on October 28, 2009.