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Three-weight codes, triple sum sets, and strongly walk regular graphs

Designs, Codes and Cryptography
Minjia Shi, Patrick Solé
Wichtige Hinweise
Communicated by J. H. Koolen.
This research is supported by National Natural Science Foundation of China (61672036), Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20).

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We construct strongly walk-regular graphs as coset graphs of the duals of three-weight codes over \(\mathbb {F}_q.\) The columns of the check matrix of the code form a triple sum set, a natural generalization of partial difference sets. Many infinite families of such graphs are constructed from cyclic codes, Boolean functions, and trace codes over fields and rings. Classification in short code lengths is made for \(q=2,3,4\).

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