Switched graphs of some strongly regular graphs related to the symplectic graph

preprint2016arXivOpen access

Abstract

Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters (2n±2(n−1)/2,2n−1±2(n−1)/2,2n−2±2(n−3)/2,2n−2±2(n−1)/2)(2^n\pm2^{(n-1)/2},2^{n-1}\pm2^{(n-1)/2},2^{n-2}\pm2^{(n-3)/2},2^{n-2}\pm2^{(n-1)/2}) are constructed for any odd n≥5n \geq 5. The construction is described in terms of geometry of quadric in projective space. The binary linear codes of the switched graphs are [2n∓2n−12,n+3,2t+1]2[2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+1}]_2-code or [2n∓2n−12,n+3,2t+2]2[2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+2}]_2-code.

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