# New Hadamard matrices of order 4p2 obtained from Jacobi sums of order 16

@article{Leung2006NewHM, title={New Hadamard matrices of order 4p2 obtained from Jacobi sums of order 16}, author={Ka Hin Leung and Siu Lun Ma and Bernhard Schmidt}, journal={J. Comb. Theory, Ser. A}, year={2006}, volume={113}, pages={822-838} }

Let p ≡ 7 mod 16 be a prime. Then there are integers a, b, c, d with a ≡ 15 mod 16, b ≡ 0 mod 4, p2 = a2 + 2(b2 + c2 + d2), and 2ab = c2 - 2cd - d2. We show that there is a regular Hadamard matrix of order 4p2 provided that p = a ± 2b or p = a + δ12b + 4δ2c + 4δ1δ2d with δi = ±1.

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