A new nonbinary sequence family with low correlation and large size

Let \begin{document} $p$ \end{document} be an odd prime, \begin{document} $n≥q3$ \end{document} and \begin{document} $k$ \end{document} positive integers with \begin{document} $e=\gcd(n,k)$ \end{document} . In this paper, a new family \begin{document} $\mathcal{S}$ \end{document} of \begin{document} $p$ \end{document} -ary sequences with period \begin{document} $N=p^n-1$ \end{document} is proposed. The sequences in \begin{document} $\mathcal{S}$ \end{document} are constructed by adding a \begin{document} $p$ \end{document} -ary sequence to its two decimated sequences with different phase shifts. The correlation distribution among sequences in \begin{document} $\mathcal{S}$ \end{document} is completely determined. It is shown that the maximum magnitude of nontrivial correlations of \begin{document} $\mathcal{S}$ \end{document} is upper bounded by \begin{document} $p^e\sqrt{N+1}+1$ \end{document} , and the family size of \begin{document} $\mathcal{S}$ \end{document} is \begin{document} $N^2$ \end{document} . Our sequence family has a large family size and low correlation.