2012/12/23 by Koji Momihara, Momihara, Koji, Qing Xiang +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05B10 #msc:05E30
paper · pdf · doi:10.48550/arxiv.1212.5752
14pages
arxiv created 2012/12/23 · arxiv updated 2012/12/27
We give two "lifting" constructions of strongly regular Cayley graphs. In the first construction we "lift" a cyclotomic strongly regular graph by using a subdifference set of the Singer difference set. The second construction uses quadratic forms over finite fields and it is a common generalization of the construction of the affine polar graphs \citeCK86 and a construction of strongly regular Cayley graphs given in \citeFWXY. The two constructions are related in the following way: The second construction can be viewed as a recursive construction, and the strongly regular Cayley graphs obtained from the first construction can serve as starters for the second construction. We also obtain association schemes from the second construction.