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

• 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
• Institution: Nanyang Technological University

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.