Four families of binary sequences with low correlation and large linear complexity

Abstract

In this paper, four new families S 1, S 2, S 3 and S 4 of binary sequences of period 2 n -∈1 with low correlation are presented, where S 1, S 3 are defined for odd n, and S 2, S 4 for even n. The family S 1 has six-valued correlations, while S 2 and S 3 have either six-valued correlations or eight-valued correlations, and S 4 has either eight-valued or ten-valued, depending on the choice of parameters. © 2008 Springer-Verlag Berlin Heidelberg.