Published online by Cambridge University Press: 15 May 2026
This chapter studies linear ternary codes generated by strongly regular signed graphs, connections between signed graphs and line systems in Euclidean space with fixed angles, and links between the spectrum of signed graphs and the skew spectrum of associated oriented graphs. We provide general characterizations and concrete constructions of efficient ternary codes, showing that those derived from adjacency matrices of strongly regular signed graphs are often optimal or satisfy conditions guaranteeing high performance, with the ternary Golay code as a notable example. The chapter also gives an upper bound on the size of line systems with specified angular properties, achieved exactly when the system corresponds to a signed graph with two eigenvalues. A central contribution of the part concerning oriented graphs is a fundamental spectral correspondence between signed graphs and associated oriented graphs, which enables the latter to be studied through the spectral theory of the former and is illustrated through several examples.
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