Generalized bilinear forms graphs and MDR codes

Li-Ping Huang

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arXiv · 1705.07083

Generalized bilinear forms graphs and MDR codes

Li-Ping Huang

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Abstract

We investigate the generalized bilinear forms graph $\Gamma_d$ over a residue class ring $\mathbb{Z}_{p^s}$. We show that $\Gamma_d$ is a connected vertex transitive graph, and completely determine its independence number, clique number, chromatic number and maximum cliques. We also prove that cores of both $\Gamma_d$ and its complement are maximum cliques. The graph $\Gamma_d$ is useful for error-correcting codes. We show that every largest independent set of $\Gamma_d$ is both an MRD code over $\mathbb{Z}_{p^s}$ and a usual MDS code. Moreover, there is a largest independent set of $\Gamma_d$ to be a linear code over $\mathbb{Z}_{p^s}$.

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Li-Ping Huang. 2017-05-19. Generalized bilinear forms graphs and MDR codes. https://arxiv.org/abs/1705.07083

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