Study On The Linear Complexity And K-error Linear Complexity Of Binary Sequences With Period 2~n

This paper mainly produces one new method to study the linear complexity and k-error linear complexity of binary sequences with period 2ⁿ. Under this new method,the concepts of the linear complexity and k-error linear complexity are more simpler.For the linear complexity of binary sequences with period 2ⁿ,we study it from its generating function.Using the change 1+x=z,we obtain another expression to the linear complexity of binary sequences with period 2ⁿ.We will find the expression and the property of the linear complexity are very intuitional.We can get a lot of new qualities easily,and simplify the original conclusions.In the third chapter,we simplify the G-C Algorithm.For the k-error linear complexity of binary sequences with period 2ⁿ, the relationship between the linear complexity and k-error linear complexity is studied.The equation minerror(a)=2^W_H(N-LC(a)) is proved again. And a super-boundary of LC_minerror(a)(a) is got,where LC(a)≥2.An algorithm for the k-error linear complexity and corresponding critical error sequence of binary sequences with period 2ⁿ is given.The problem about counting the number of critical error sequences is discussed.At last a new algorithm for the k-error linear complexity is proved where k=minerror(a)=2^W_H(N-LC(a)),this algorithm saves more operations and spaces than the original algorithm.