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

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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Bibliographic Details
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
Description
Summary: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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