New p-ary sequence family with low correlation and large linear span

Abstract

In this paper, for an odd prime p and positive integers n, m, and e such that n = me, a new family $${\mathcal{S}}$$ of p-ary sequences of period p n − 1 with low correlation and large linear span is constructed. It is shown that $${\mathcal{S}}$$ has maximum correlation $${1+p^{n+2e\over 2}}$$, family size p n , and maximal linear span $${{(m+3)n\over 2}}$$. When m is even, the proposed family $${\mathcal{S}}$$ contains Tang, Udaya, and Fan’s construction as a subset. Furthermore, when n is even and $${e=1, \mathcal{S}}$$ has the same correlation and family size, but larger linear span compared with the construction by Seo, Kim, No, and Shin.