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Linear complexity is an important standard to scale the randomicity of stream ciphers. The distribution function of a sequence complexity measure gives the function expression for the number of sequences with a given complexity measure value. In this paper, we mainly determine the distribution function of sequences with period N =2 n l = over F q using Discrete Fourier Transform (DFT) , where n and the characteristics of F q are odd primes, gcd ( n, q ) = 1 and q is a primitive root modulo 2 n l . The results presented can be used to study the randomness of periodic sequences and the analysis and design of stream cipher.
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