On The F-Complexity?Cross-Correlation And Linear Complexity Of Some Pseudorandom Sequences

It is very difficult to construct large family of pseudorandom binary se-quences with large f-complexity and small cross-correlation measure.In this paper we give two large families of binary sequences and show that they enjoy largef-complexity and small cross-correlation measure by using the Legendre symbol and estimates for character sums of polynomials where p is a prime number,(?)denotes the Legendre symbol of modulus p,b is a quadratic non-residue of the module p,z denote z multiplication inverse of the module p,satisfied 1?z?p-1 and zz ? 1(mod p).Linear complexity profile is an important criterion to judge pseudo-randomness.In this paper we shall study the linear complexity profile of the families of k symbols.We construct k sequence Ep=(e1,…,ep)?ZkP by using the original root where p is a prime number,g is a primitive root modulo p,indg(x)denote the index ofx to the base g so that gindg(x)?x(mod p).We study the following sequence EN=(e1,…,eN)?ZkN of k symbols by using polynomials over finite field and the generalized cyclotomic class for n=1,2,…,N,and fixed elements A,B?ZkWe prove that the linear complexity profiles of Ep and EN of k symbols are "good".