The Linear Complexity Of Several Classes Of Balanced Periodic Sequences

The linear complexity is an important indicator that measures good or bad property of the pseudo-random sequence. The sequence with good linear complexity has been widely applied in the communication system and cryptography. In the paper, we always assume that p and q are distinct odd primes, m, n are natural numbers, unless otherwise stated, gcd (p-1, q-1)=4.Firstly, we construct a class of balanced binary sequences of period pm+1qn+1 by using Whiteman generalized cyclotomy of order 4 and the theory of quadratic residue. We determine the linear complexity of the sequences by using the auxiliary polynomial. The values of p, q are discussed. In addition, the minimal polynomials of the sequences are given. Moreover, The linear complexity and minimal polynomials of binary balanced sequences constructed by Whiteman generalized cyclotomy of order e (e/2 is even) also is considered.Secondly, we investigate another class of binary balanced sequences of period pm+1qn+l by using Whiteman generalized cyclotomy of order 4 and the theory of quadratic residue. Let ? be a primitive pq th root of unity over extension field of GF(1), we fix a common primitive root g of both p and q, and let y be an integer satisfying, y= g(mod p), y=1(mod q). Then Uo= (g) is a subgroup of the multiplicative group Z. Define the values of We mainly discuss the values of T4(?)=(T(?),T(?y),T(?y2),T(?y3)). The linear complexity and minimal polynomials of the sequences are calculated.Finally, we make a summary and outlook for this thesis. In order to obtain sequences with good linear complexity and autocorrelation property, we hope to construct new balanced sequences of period pm+1qn+1 by using Whiteman generalized cyclotomy of order e over the field GF(q).