Relations Among Generalized Hadamard Matrices, Relative Difference Sets, and Maximal Length Linear Recurring Sequences

It was established in (5) that the existence of a Hadamard matrix of order 4 t is equivalent to the existence of a symmetrical balanced incomplete block design with parameters v = 4 t — 1, k = 2 t — 1, and λ = t — 1. A block design is completely characterized by its so-called incidence matrix. The existence of a block design with parameters v , k , and λ such that the corresponding incidence matrix is cyclic was shown in (3) to be equivalent to the existence of a cyclic difference set with parameters v , k , and λ. For certain values of the parameters, Hadamard matrices, block designs, and difference sets do coexist.