Applications of coding and design theory to constructing the maximum resilient systems of functions

Some ideas, methods, and results of coding and design theory, especially a duality in bounding the optimal size of codes and designs (orthogonal arrays), are used to solve a new problem connected with randomized systems of functions. The problem is reduced to the minimization of the size of certain combinatorial designs, which we call split orthogonal arrays (SOA). We extend the linear programming method of Delsarte (1973) to obtain a lower bound and an upper bound on the systems of functions.