On splitting sets in block designs and finding roots of polynomials

Abstract

The general notion of t-splitting sets is introduced within the context of combinatorial block designs. A greatest lower bound on cardinality of such sets, and an upper bound on cardinality of the smallest such set in a given design are established. The abstraction of t-splitting sets is shown to provide a natural framework for the analysis of the problem of finding roots of polynomials over finite fields, and elementary concepts from design theory are applied to re-examine and extend some existing results in this area.