A New Family of $p$-Ary Sequences With Low Correlation Constructed From Decimated Sequences

In this paper, for an odd prime $p$ and an integer $n \geq 3$, a new family of $p$ -ary sequences of period ${{p^{n}-1} \over {2}}$ with low correlation is constructed. The new family is constructed by shifts and additions of two decimated sequences of a $p$-ary $m$ -sequence, and its family size is $2(p^{n}-1)$. The complete correlation distribution of this new family is derived. It is also shown that the family is optimal with respect to the parameter $\theta_{{\rm rms}}$, which denotes the root mean square of all nontrivial correlations. Compared with the known sequence families, our sequence family is new and has a larger family size, which is four times of its period.