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 +1 and +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 +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.

In this paper, a new family S(r) of 2n binary sequences of period 2n-1 is proposed, where n ≡ 2 mod 4 and gcd(r, 2n/2-1)=1. The presented family takes 4-valued out-of-phase auto- and cross-correlation values -1, 2n/2-1, and 2n/2+1-1, and its correlation distribution is determined. For r=2(n-2)/4-1, each sequence in S(r), except the unique ideal autocorrelation sequence in the family, is proved to have a large linear span n2n/2-2, whilst the linear span of the latter is n2(n-2)/4-1.