Abstract
<p style='text-indent:20px;'>In this paper we introduce the notion of orbit matrices of integer matrices such as Seidel and Laplacian matrices of some strongly regular graphs with respect to their permutation automorphism groups. We further show that under certain conditions these orbit matrices yield self-orthogonal codes over finite fields <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_q $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ q $\end{document}</tex-math></inline-formula> is a prime power and over finite rings <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{Z}_m $\end{document}</tex-math></inline-formula>. As a case study, we construct codes from orbit matrices of Seidel, Laplacian and signless Laplacian matrices of strongly regular graphs. In particular, we construct self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of the Higman-Sims and McLaughlin graphs.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
