Signed Difference Sets
Daniel M. Gordon

TL;DR
This paper introduces signed difference sets, a generalization of difference sets and circulant weighing matrices, exploring their properties and existence conditions in group theory.
Contribution
It defines signed difference sets and investigates their existence, expanding the understanding of difference set generalizations in algebraic combinatorics.
Findings
Signed difference sets generalize difference sets and circulant weighing matrices.
Existence results for certain classes of signed difference sets are provided.
The paper identifies new cases of interest for signed difference sets.
Abstract
A difference set in a group of order is a subset of such that in the group ring satisfies where . If , where the , satisfies the same equation, we will call it a signed difference set. This generalizes both difference sets (all ) and circulant weighing matrices ( cyclic and ). We will show that there are other cases of interest, and give some results on their existence.
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Taxonomy
Topicsgraph theory and CDMA systems
