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Linear codes from quadratic forms

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime power q, we present a class of linear codes over finite fields \(F_q\) with quadratic forms via a general construction and then determine the explicit complete weight enumerators of these linear codes. Our construction covers some related ones via quadratic form functions and the linear codes may have applications in cryptography and secret sharing schemes.

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Acknowledgements

The authors acknowledge the patient referees for their valuable and constructive comments which helped to improve this work.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, Gansu, People’s Republic of China

    Xiaoni Du & Yunqi Wan

Authors
  1. Xiaoni Du
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  2. Yunqi Wan
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Corresponding author

Correspondence to Yunqi Wan.

Additional information

X. Du was partially supported by the National Natural Science Foundation of China (Grant Nos. 61462077 and 61662071), the Natural Science Foundation of Shanghai (No. 16ZR1411200) and Anhui Provincial Natural Science Foundation (No. 1608085MF143).

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Du, X., Wan, Y. Linear codes from quadratic forms. AAECC 28, 535–547 (2017). https://doi.org/10.1007/s00200-017-0319-x

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  • DOI: https://doi.org/10.1007/s00200-017-0319-x

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