The Correlation Distribution of Quaternary Sequences of Period $2(2^n-1)$

Family A is a family of sequences of period 2
ⁿ
- 1 over Zi, the ring of integers modulo 4. This family has optimal correlation properties and its correlation distribution is well known. Two related families of quaternary sequences are the families B and C. These are families of sequences over Z
₄
of period 2(2
ⁿ
- 1). In recent years, new families of quaternary sequences of period 2(2
ⁿ
- 1) have been constructed by modifying the sequence families B and C in a nonlinear way. This has resulted in a new family D of sequences of period 2(2
ⁿ
- 1) which has optimal correlation properties, but until now the correlation distribution of this family has not been known. In this paper, we completely determine the correlation distribution of family D by making use of properties of exponential sums.