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Designs, Codes and Cryptography

, Volume 86, Issue 4, pp 817–833 | Cite as

A link between combinatorial designs and three-weight linear codes

  • Oktay OlmezEmail author
Article

Abstract

In this paper, we show that partial geometric designs can be constructed from certain three-weight linear codes, almost bent functions and ternary weakly regular bent functions. In particular, we show that existence of a family of partial geometric difference sets is equivalent to existence of a certain family of three-weight linear codes. We also provide a link between ternary weakly regular bent functions, three-weight linear codes and partial geometric difference sets.

Keywords

Partial geometric designs Partial geometric difference sets Weakly regular bent functions Almost bent functions Plateaued functions Three-weight linear codes Strongly regular graphs 

Mathematics Subject Classification

05B05 05B10 06E30 11T71 

Notes

Acknowledgements

We are grateful to anonymous referees for numerous helpful comments which make us to improve the exposition of the paper.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAnkara UniversityAnkaraTurkey

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