New Family of Binary Sequences with Low Correlation

Abstract

In this paper, a new family of binary sequences of period 2n-1 with low correlation is proposed for integer n = em and even m. The new family has family size 2n + 1 and maximum nontrivial correlation 2n+e/2 + 1 and 2n+e-1/2 + 1 for even and odd e respectively. Especially, for n = 2m and 3m, we obtain a new family of binary sequences with maximum nontrivial correlation 2n/2 + 1 + 1, and the obtained family is one of the binary families with best correlation among the known families with family size no less than their period 2n-1 for even n. Moreover, the correlation distribution of the new family is also determined.