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.
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The research supported by NSF of China (No. 10071029).
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Xia, M., Xia, T. & Seberry, J. A New Method for Constructing Williamson Matrices. Des Codes Crypt 35, 191–209 (2005). https://doi.org/10.1007/s10623-005-6401-6
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DOI: https://doi.org/10.1007/s10623-005-6401-6