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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