A New Method for Constructing Williamson Matrices

Authors:
Mingyuan Xia;Tianbing Xia;Jennifer Seberry
Affiliations:
Department of Mathematics, Central China Normal University, Wuhan, China 430079;School of IT & CS, University of Wollongong, Australia 2500;School of IT & CS, University of Wollongong, Australia 2500
Venue:
Designs, Codes and Cryptography
Year:
2005

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Abstract

For every prime power q 驴 1 (mod 4) we prove the existence of (q; x, y)-partitions of GF(q) with q=x2+4y2 for some x, y, which are very useful for constructing SDS, DS and Hadamard matrices. We discuss the transformations of (q; x,y)-partitions and, by using the partitions, construct generalized cyclotomic classes which have properties similar to those of classical cyclotomic classes. Thus we provide a new construction for Williamson matrices of order q2.