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

  • Minjia ShiEmail author
  • Patrick Solé
Article
  • 23 Downloads

Abstract

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 \(q=2,3,4\).

Keywords

Strongly walk-regular graphs Three-weight codes Triple sum sets 

Mathematics Subject Classification

Primary 05 E 30 Secondary 94 B 05 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical Sciences of Anhui UniversityAnhuiPeople’s Republic of China
  2. 2.Aix Marseille Univ, CNRS, Centrale Marseille, I2MMarseilleFrance

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