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.

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Persistent URL dx.doi.org/10.1016/0012-365X(90)90274-L
Journal Discrete Mathematics
Citation
Van Oorschot, P, & Vanstone, S.A. (S. A.). (1990). On splitting sets in block designs and finding roots of polynomials. Discrete Mathematics, 84(1), 71–85. doi:10.1016/0012-365X(90)90274-L