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

Abstract : We construct strongly walk-regular graphs as coset graphs of the duals of three-weight codes over 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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https://hal.inria.fr/hal-02411038
Contributor : Patrick Sol'E <>
Submitted on : Tuesday, December 17, 2019 - 3:54:14 AM
Last modification on : Tuesday, December 1, 2020 - 3:34:02 PM
Long-term archiving on: : Wednesday, March 18, 2020 - 12:42:31 PM

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Patrick Sole, Minjia Shi. Three-weight codes, triple sum sets, and strongly walk regular graphs. Designs, Codes and Cryptography, Springer Verlag, 2019, 87, pp.2395 - 2404. ⟨10.1007/s10623-019-00628-7⟩. ⟨hal-02411038⟩

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