5값 상호상관함수를 갖는 비선형수열의 함숫값 분포 및 선형스팬 분석

Abstract

In this thesis we analyze the cross-correlation values and the linear span of nonlinear sequences based on the trace function and the decimation. The study about the cross-correlation function and linear span of pseudorandom binary sequences is important area of the wireless communication technology and the security and code system. In particular cross-correlation function has to do with the good communication which is possible by minimizing the multiple-access-interference. Large linear span makes difficult to predict, so this study is related to the security and code system. It is to be known that the linear span of No sequence is larger than the linear span of GMW sequence. We prove the linear span of the sequence generated by GMW sequence and No sequence is larger than the linear span of GMW sequence in Chapter 3. The values of sigma_(tau=0) ^(2n-2) (C_d (tau)+1)), sigma_(tau=0) ^(2n-2) (C_d (tau)+1))^2, sigma_(tau=0) ^(2n-2) (C_d (tau)+1))^3 are important to know the distribution of the cross-correlation values. To find the value of sigma_(tau=0) ^(2n-2) (C_d (tau)+1))^3, it is essential to know the number of the roots of the equation (x+1)^d=x^d+1. It is presented in Chapter 4. In Chapter 5, we analyze the cross-correlation values of the nonlinear sequence S_a ^r (t) with the decimation d=2^(m-2)(2^m+3) and the distribution of the cross-correlation values. This sequence has five cross-correlation values, -1-2^m, -1, -1+2^m, -1+2·2^m and -1+3·2^m. In Chapter 6, we prove that the linear span of the sequence S_a ^r (t) is larger than the linear span of GMW sequence.