On a Class of Symmetric Balanced Generalized Weighing Matrices

Authors:
H. Kharaghani
Affiliations:
Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada
Venue:
Designs, Codes and Cryptography
Year:
2003

Citing 4
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Abstract

Let q be a prime power and m a positive integer. A construction method is given to “multiply” the parametrs of an ω-circulant BGW(v=1+q+q2+·+qm, qm, qm−qm−1) over the cyclic group Cn of order n with (q−1)/n being an even integer, by the parameters of a symmetric BGW(1+qm+1, qm+1, qm+1−qm) with zero diagonal over a cyclic group Cvn to generate a symmetric BGW(1+q+·+q2m+1,q2m+1,q2m+1−q2m) with zero diagonal, over the cyclic group Cn. Applications include two new infinite classes of strongly regular graphs with parametersSRG(36(1+25+·+252m+1),15(25)2m+1,6(25)2m+1,6(25)2m+1), and SRG(36(1+49+·+492m+1),21(49)2m+1,12(49)2m+1,12(49)2m+1).