Introduction to finite fields and their applications
Introduction to finite fields and their applications
An infinite class of supplementary difference sets and Williamson matrices
Journal of Combinatorial Theory Series A - Series A
Difference families from lines and half lines
European Journal of Combinatorics
A New Method for Constructing Williamson Matrices
Designs, Codes and Cryptography
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For every prime power q ≡ 7 mod 16, we obtain the (q; a, b, c, d) - partitions of GF(q), with odd integers a, b, c, d, a ≡ ± 1 mod 8 such that q = a2 +2(b2 + c2 + d2) and d2 = b2 + 2ac + 2bd. Hence for each value of q the contruction of SDS becomes equivalent to building a (q; a, b, c, d)-partition. The latter is much easier than the former. We give a new construction for an infinite family of regular Hadamard matrices of order 4q2 by 16th power cyclotomic classes.