A New Method for Constructing Williamson Matrices |
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Authors: | Email author" target="_blank">Mingyuan?XiaEmail author Tianbing?Xia Jennifer?Seberry |
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Institution: | (1) Department of Mathematics, Central China Normal University, Wuhan, Hubei, 430079, China;(2) School of IT & CS, University of Wollongong, NSW, 2500, Australia |
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Abstract: | For every prime power q 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.The research supported by NSF of China (No. 10071029). |
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Keywords: | difference sets supplementary difference sets partition |
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