| 低汉明重量序列的分布 |
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| 引用本文： | 李江华,李桥,赵怀军.低汉明重量序列的分布[J].数学进展,2021(2):303-308. |
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| 作者姓名： | 李江华 李桥 赵怀军 |
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| 作者单位： | 西安理工大学理学院应用数学系 |
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| 基金项目： | Supported by NSFC (Nos.2017YFF0104401,413618022);Natural Science Foundation of Shaanxi Province (No.2019JQ333)。 |
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| 摘 要： | 数n的汉明重量是指n的二进制字符串表达式中数字1的个数,用Ham(n)来表示.低汉明重量序列在密码系统和编码理论中有非常广泛的应用.本文建立了低汉明重量数的序列表达式,并且利用指数和的上界以及Erdos-Turan不等式证明低汉明重量序列的均匀分布性质,从而确保密码算法的随机性和运算效率.
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| 关 键 词： | 低汉明重量 均匀分布 指数和 |
On the Distribution of Low Hamming Weight Sequence |
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| LI Jianghua,LI Qiao,ZHAO Huaijun.On the Distribution of Low Hamming Weight Sequence[J].Advances in Mathematics,2021(2):303-308. |
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| Authors: | LI Jianghua LI Qiao ZHAO Huaijun |
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| Institution: | (Department of Applied Mathematics,School of Sciences,Xi'an University of Technology,Xi'an,Shaanxi,710054,P.R.China) |
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| Abstract: | The Hamming weight of the number n represents the number of digits 1 in the binary string representation,denoted by Ham(n).Low Hamming weight numbers are universally applied in many cryptosystems and the coding theory.In this paper,we construct a sequence expression of the low Hamming weight numbers,and prove the uniform distribution of the low Hamming weight sequence using the upper bound of exponential sums and the Erdos-Turan inequality,which can ensure the randomness and the efficiency of the cryptographic algorithms. |
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| Keywords: | low Hamming weight uniform distribution exponential sums |
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