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Designs, Codes and Cryptography

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08-02-2017

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

Authors: Alice M. W. Hui, B. G. Rodrigues

Published in: Designs, Codes and Cryptography | Issue 1/2018

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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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Title: Switched graphs of some strongly regular graphs related to the symplectic graph
Authors: Alice M. W. Hui
B. G. Rodrigues
Publication date: 08-02-2017
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 1/2018
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0340-x

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

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