On supplementary difference sets

Authors

Jennifer Seberry, University of WollongongFollow

Publication Details

Jennifer Seberry Wallis, On supplementary difference sets, Aequationes Mathematicae, 8, (1972), 242-257.

Abstract

Given a finite abelian group V and subsets S₁, S₂, ... ,S_n of V, write T_i for the totality of all the possible differences between elements of S_i (with repetitions counted multiply) and T for the totality of members of all the T_i. If T contains each non-zero element of V the same number of times, then the sets S_1, S₂,...,S_n will be called supplementary difference sets.

We discuss some properties for such sets, give some existence theorems and observe their use in the construction of Hadamard matrices and balanced incomplete block designs.