Two New Families of Optimal Binary Sequences Obtained From Quaternary Sequences

In this paper, we present two optimal binary families of sequences of length 2
ⁿ
-1 and 2(2
ⁿ
-1) for odd integer n. They are obtained as the images of proposed optimal quaternary sequences under the most significant bit and the Gray maps. The first family has 2
ⁿ
+1 sequences of length 2
ⁿ
-1 and the identical correlation distribution to that of Gold sequences and Gold-like sequences, and the second family of sequences of length 2(2
ⁿ
-1) has 2
ⁿ
sequences and the same correlation values as those of Kerdock sequences.