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+q 2+·+q m, q m, q m−q m−1) over the cyclic group C n of order n with (q−1)/n being an even integer, by the parameters of a symmetric BGW(1+q m+1, q m+1, q m+1−q m) with zero diagonal over a cyclic group C vn to generate a symmetric BGW(1+q+·+q 2m+1,q 2m+1,q 2m+1−q 2m) with zero diagonal, over the cyclic group C n . 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).
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Kharaghani, H. On a Class of Symmetric Balanced Generalized Weighing Matrices. Designs, Codes and Cryptography 30, 139–149 (2003). https://doi.org/10.1023/A:1025436002985
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DOI: https://doi.org/10.1023/A:1025436002985