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 over using Discrete Fourier Transform (DFT), where and the characteristics of are odd primes, gcd and is a primitive root modulo The results presented can be used to study the randomness of periodic sequences and the analysis and design of stream cipher.
Abstract We investigate negacyclic codes over the Galois ring GR（2a,m） of length N = 2kn, where n is odd and k≥0. We first determine the structure of u-constacyclic codes of length n over the finite chain ring GR（2a, m）[u]/〈u2k ＋ 1〉. Then using a ring isomorphism we obtain the structure of negacyclic codes over GR（2a, m） of length N = 2kn （n odd） and explore the existence of self-dual negacyclic codes over GR（2a, m）. A bound for the homogeneous distance of such negacvclic codes is also given.
ZHU ShiXin 1,2,& KAI XiaoShan 1,2 1 School of Mathematics,Hefei University of Technology,Hefei 230009,China
