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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Acknowledgements
The authors would like to thank Jennifer Key and Willem Haemers for constructive remarks and suggestions. The anonymous referees are thanked for the many suggestions and corrections which have improved the presentation of the paper in both content and form. This work is based on the research supported by the National Research Foundation of South Africa (Grant Numbers 91495 and 87470).
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Communicated by J. H. Koolen.
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Hui, A.M.W., Rodrigues, B.G. Switched graphs of some strongly regular graphs related to the symplectic graph. Des. Codes Cryptogr. 86, 179–194 (2018). https://doi.org/10.1007/s10623-017-0340-x
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DOI: https://doi.org/10.1007/s10623-017-0340-x