Designs, Codes and Cryptography

, Volume 81, Issue 2, pp 283–295 | Cite as

Linear codes with two or three weights from quadratic Bent functions

  • Zhengchun Zhou
  • Nian Li
  • Cuiling Fan
  • Tor Helleseth


Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of p-ary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field \({\mathbb {F}}_p\), where p is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined.


Linear code Optimal code Bent function Quadratic form  Weight distribution 

Mathematics Subject Classification

94A24 94B35 94B15 94A55 



The authors are very grateful to the reviewers and the Editor for their comments and suggestions that improved the presentation and quality of this paper. C. Fan’s research was supported by the Natural Science Foundation of China, Proj. No. 11571285, Z. Zhou’s research was supported by the Natural Science Foundation of China, Proj. No. 61201243, the Sichuan Provincial Youth Science and Technology Fund under Grant 2015JQO004, and the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University under Grant 2013D10.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Zhengchun Zhou
    • 1
  • Nian Li
    • 2
  • Cuiling Fan
    • 1
  • Tor Helleseth
    • 2
  1. 1.School of MathematicsSouthwest Jiaotong UniversityChengduChina
  2. 2.Department of InformaticsUniversity of BergenBergenNorway

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