Study Of The 2-adic Complexity Of Several Classes Of Binary Sequences

With the development of communication and information technology,pseudo-random sequences have a wide application in communication,cryptography,radar and so on.In practical applications,the pseudo-random sequences are usually required to have good pseudo-random properties,such as long period,low correlation,high linear complexity,high 2-adic complexity,etc.The 2-adic complexity of a periodic sequence is defined as the length of the shortest feedback with carry shift register.In the ap-plication of cryptography,in order to resist the attack of the rational approximation algorithm,the pseudo-random sequence must have high 2-adic complexity.Other-wise,the whole sequence can be restored by the rational approximation algorithm if twice 2-adic complexity length of the sequence are known.Therefore,the study of constructing binary sequences with high 2-adic complexity and calculating the 2-adic complexity of binary sequences have a good theoretical significance and application background.In the thesis,we will analyze the 2-adic complexity of a class of binary sequences with period 4and good correlation property by using the calculation method pro-posed by Hu,and also we will analyze the 2-adic complexity of two kinds of binary sequences with period 2p~2and 2p~m and high linear complexity by using the calculation method proposed by Xiong et al.In detail,1.By using Hu's method and Gauss sum,the 2-adic complexity of a class of binary sequence with good correlation property,which was constructed by using inter-leaving technique,is determined.Our results show that this class of binary sequences have high 2-adic complexity,which means that it can resist the attack of rational approximation algorithm.2.By a method proposed by Xiong et al.,the 2-adic complexity of a class of binary sequence with period 2p~2 and high linear complexity is determined.And our results show that the 2-adic complexity of this class of binary sequences can reach its maximum in some cases.Furthermore,we calculate the 2-adic complexity of a class of binary sequences with period 2p~m and high linear complexity by the same way.Our results show that the 2-adic complexity of this class of binary sequences can reach its maximum in the case of p?±1(mod 8).