A Construction of a New Family of $M$-ary Sequences With Low Correlation From Sidel'nikov Sequences

In this paper, a new family of
M
-ary sequences of period
p
ⁿ
-1 is proposed. The proposed family is constructed by the addition of cyclic shifts of an
M
-ary Sidel'nikov sequence and its reverse sequence. The number of sequences contained in this family is about (
M
-1)
²
times of their period and the maximum magnitude of their correlation values is upper bounded by 4 √(
p
ⁿ
)
+5.