A new nonbinary sequence family with low correlation and large size

Abstract

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