08.02.2017 | Ausgabe 1/2018
Switched graphs of some strongly regular graphs related to the symplectic graph
- Zeitschrift:
- Designs, Codes and Cryptography > Ausgabe 1/2018
Wichtige Hinweise
Communicated by J. H. Koolen.
Abstract
By applying a method of Godsil and McKay to some graphs related to the symplectic graph, two series of new infinite families of switched strongly regular graphs with parameters \(\big (2^n\pm 2^{\frac{n-1}{2}},2^{n-1}\pm 2^{\frac{n-1}{2}},2^{n-2} \pm 2^{\frac{n-3}{2}},2^{n-2}\pm 2^{\frac{n-1}{2}}\big )\) are constructed for \(n \ge 5\), where n is odd. The construction is described in terms of the geometry of quadrics in the projective space. The binary linear codes of these switched graphs have parameters \(\big [2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+1}\big ]_2\) and \(\big [2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+2}\big ]_2\) respectively.
