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Erd?s-Turán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.“,”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 Erd?s-Turán inequality,which can ensure the randomness and the efficiency of the cryptographic algorithms.