Generalized bilinear forms graphs and MDR codes

2017/05/19 by Liping Huang, Huang, Li-Ping
Computer Science · #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1705.07083

openalex publication_date 2017/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the generalized bilinear forms graph Γ_d over a residue class ring ℤ_p^s. We show that Γ_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 Γ_d and its complement are maximum cliques. The graph Γ_d is useful for error-correcting codes. We show that every largest independent set of Γ_d is both an MRD code over ℤ_p^s and a usual MDS code. Moreover, there is a largest independent set of Γ_d to be a linear code over ℤ_p^s.

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