At most three-weight binary linear codes from generalized Moisio’s exponential sums
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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.
KeywordsBinary linear codes Gauss sums Gauss periods Secret sharing schemes
Mathematics Subject Classification11T71 11T24
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).