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08.02.2017 | Ausgabe 1/2018

Designs, Codes and Cryptography 1/2018

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

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 1/2018
Autoren:
Alice M. W. Hui, B. G. Rodrigues
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.

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