Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternary sequences have large linear complexity to resist Reeds and Sloane algorithm attack effectively.
Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.
