Extending Brickell–Davenport theorem to non-perfect secret sharing schemes - Farràs, Oriol; Padró, Carles (Designs, codes, and cryptography, 2015)
One important result in secret sharing is the Brickell–Davenport theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. We present a generalization of the Brickell–Davenport theorem to the general case, in which non-perfect schemes are also considered. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated with matroids. Some optimality properties of such schemes are discussed.