Robinson’s Theorem

Abstract

In trying to decide which orthogonal designs to look for, it would be useful to formulate, and hopefully prove valid, some general principles of the sort, “All orthogonal designs of a certain type exist in certain orders”. The Hadamard conjecture, the skew-Hadamard conjecture, the weighing matrix conjecture, and other conjectures that have been made, and extensively verified, provide some solid information which must be dealt with in order to state such principles. We have seen singularly unsuccessful in formulating correct principles of a general nature; some conjectures that we have made in the light of those principles have proved to be false.