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Recent results and problems on constructions of linear codes from cryptographic functions

  • SI: Boolean Functions and Their Applications 2019
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Abstract

Linear codes have a wide range of applications in the data storage systems, communication systems, consumer electronics products since their algebraic structure can be analyzed and they are easy to implement in hardware. How to construct linear codes with excellent properties to meet the demands of practical systems becomes a research topic, and it is an efficient way to construct linear codes from cryptographic functions. In this paper, we will introduce some methods to construct linear codes by using cryptographic functions over finite fields and present some recent results and problems in this area.

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Acknowledgments

The authors thank Lilya Budaghyan and Tor Helleseth for their very nice invitation to the conference BFA 2019 (dedicated to the 70th birthday of Claude Carlet) and their excellent organization. This work was supported by the National Natural Science Foundation of China (Nos. 61702166, 61761166010) and National Natural Science Foundation of Hubei Province of China (No. 2017CFB143).

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Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Nian Li

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Nian Li

  3. Department of Mathematics, University of Paris VIII, 93526, Saint-Denis, France

    Sihem Mesnager

  4. University of Paris XIII, Sorbonne Paris Cité, 93430, LAGA, UMR 7539, CNRS, France

    Sihem Mesnager

  5. France Telecom Paris, 91120, Palaiseau, France

    Sihem Mesnager

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  1. Nian Li
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  2. Sihem Mesnager
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Correspondence to Nian Li.

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This paper is dedicated to celebrate Prof. Claude Carlet’s 70 birthday.

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This article is part of the Topical Collection on Boolean Functions and Their Applications IV

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Li, N., Mesnager, S. Recent results and problems on constructions of linear codes from cryptographic functions. Cryptogr. Commun. 12, 965–986 (2020). https://doi.org/10.1007/s12095-020-00435-1

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