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At most three-weight binary linear codes from generalized Moisio’s exponential sums

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Abstract

In this paper, we evaluate two classes of new exponential sums, which are viewed as generalized Moisio’s exponential sums in contrast to the results by Heng and Yue (IEEE Commun Lett 19:1488–1491, 2015) and Moisio (Finite Fields Appl 15:644–651, 2009). As applications, we present two classes of binary linear codes with two wights or three weights. These codes can be used in secret sharing schemes and authentication codes.

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Acknowledgements

The paper is supported by National Natural Science Foundation of China (Nos. 61772015, 61602144, 11661013, 11661014), the Guangxi Natural Sciences Foundation (Nos. 2016GXNSFCA380014, 2016GXNSFDA380017), Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-010), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Nos. KYCX17_0225, KYCX18_0241), and the Fundamental Research Funds for the Central Universities (No. NZ2018005).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, Jiangsu, People’s Republic of China

    Yansheng Wu, Qin Yue & Xueying Shi

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, People’s Republic of China

    Yansheng Wu, Qin Yue & Xueying Shi

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  1. Yansheng Wu
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  2. Qin Yue
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  3. Xueying Shi
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Correspondence to Qin Yue.

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Communicated by C. Ding.

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Wu, Y., Yue, Q. & Shi, X. At most three-weight binary linear codes from generalized Moisio’s exponential sums . Des. Codes Cryptogr. 87, 1927–1943 (2019). https://doi.org/10.1007/s10623-018-00595-5

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