New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16

Let p=7 mod 6 be a prime. Then there are integers a,b,c,d with a=15 mod 6, b= 0 mod 4, p^2=a^2+2(b^2+c^2+d^2), and 2ab=c^2-2cd-d^2. 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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Main Authors:	Bernhard, Schmidt, Ma, Siu Lun, Leung, Ka Hin
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2009
Subjects:	DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics
Online Access:	https://hdl.handle.net/10356/92119 http://hdl.handle.net/10220/6066
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Institution:	Nanyang Technological University
Language:	English

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spelling	sg-ntu-dr.10356-921192023-02-28T19:30:07Z New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16 Bernhard, Schmidt Ma, Siu Lun Leung, Ka Hin School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics Let p=7 mod 6 be a prime. Then there are integers a,b,c,d with a=15 mod 6, b= 0 mod 4, p^2=a^2+2(b^2+c^2+d^2), and 2ab=c^2-2cd-d^2. 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. Accepted version 2009-08-12T06:14:11Z 2019-12-06T18:17:45Z 2009-08-12T06:14:11Z 2019-12-06T18:17:45Z 2006 2006 Journal Article Schmidt, B., Ma, S. L., & Ka, H. L. (2006). New Hadamard Matrices of Order 4p^2 obtained from Jacobi Sums of Order 16. Journal of Combinatorial Theory Series A, 113(5), 822-838. 0097-3165 https://hdl.handle.net/10356/92119 http://hdl.handle.net/10220/6066 10.1016/j.jcta.2005.07.011 en Journal of combinatorial theory series A. Journal of Combinatorial Theory Series A © copyright 2006 Elsevier. The journal's website is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WHS-4JRVFR6-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=21abc0c7c783ebc249d071647769d03e. 18 p. application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics
spellingShingle	DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics Bernhard, Schmidt Ma, Siu Lun Leung, Ka Hin New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16
description	Let p=7 mod 6 be a prime. Then there are integers a,b,c,d with a=15 mod 6, b= 0 mod 4, p^2=a^2+2(b^2+c^2+d^2), and 2ab=c^2-2cd-d^2. 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.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Bernhard, Schmidt Ma, Siu Lun Leung, Ka Hin
format	Article
author	Bernhard, Schmidt Ma, Siu Lun Leung, Ka Hin
author_sort	Bernhard, Schmidt
title	New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16
title_short	New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16
title_full	New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16
title_fullStr	New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16
title_full_unstemmed	New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16
title_sort	new hadamard matrices of order 4p^2 obtained from jacobi sums of order 16
publishDate	2009
url	https://hdl.handle.net/10356/92119 http://hdl.handle.net/10220/6066
_version_	1759855140989304832

New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16

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