Generic Construction of Quaternary Sequences of Period $2N$ With Low Correlation From Quaternary Sequences of Odd Period $N$

In this paper, a simple but generic method is proposed for transforming any family of quaternary sequences, with low correlation, of any odd period
N
to another family of quaternary sequences of period 2N with low correlation. As an application of the generic method to sequence Family A, a new optimal quaternary sequence family with length 2(2
ⁿ
-1), family size 2
ⁿ
+1 , and maximal nontrivial correlation value 2
^[(
n+1)/2]+2, where
n
is an odd integer, is obtained. Most notably, unlike all the known optimal quaternary sequence families, the new family has a unique property that the odd integers 1, 3 and the even integers 0, 2 are allocated alternatively in all the sequences.