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

Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jcta.2005.07.011

Title:	New Hadamard matrices of order 4 p2 obtained from Jacobi sums of order 16
Authors:	Leung, K.H. Ma, S.L. Schmidt, B.
Keywords:	Difference families Hadamard matrices Jacobi sums
Issue Date:	Jul-2006
Citation:	Leung, K.H., Ma, S.L., Schmidt, B. (2006-07). New Hadamard matrices of order 4 p2 obtained from Jacobi sums of order 16. Journal of Combinatorial Theory. Series A 113 (5) : 822-838. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcta.2005.07.011
Abstract:	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 2 ab = c2 - 2 cd - d2. We show that there is a regular Hadamard matrix of order 4 p2 provided that p = a ± 2 b or p = a + δ1 2 b + 4 δ2 c + 4 δ1 δ2 d with δi = ± 1. © 2006 Elsevier Inc. All rights reserved.
Source Title:	Journal of Combinatorial Theory. Series A
URI:	http://scholarbank.nus.edu.sg/handle/10635/103601
ISSN:	00973165
DOI:	10.1016/j.jcta.2005.07.011
Appears in Collections:	Staff Publications

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