Finiteness of circulant weighing matrices of fixed weight

Authors:
Ka Hin Leung;Bernhard Schmidt
Affiliations:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260, Republic of Singapore;Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

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Abstract

Let n be a fixed positive integer. Every circulant weighing matrix of weight n arises from what we call an irreducible orthogonal family of weight n. We show that the number of irreducible orthogonal families of weight n is finite and thus obtain a finite algorithm for classifying all circulant weighing matrices of weight n. We also show that, for every odd prime power q, there are at most finitely many proper circulant weighing matrices of weight q.