New nonbinary sequence families with low correlation, large size, and large linear span (Q533455)

Let \(p\) be an odd prime and \(n=(2m+1)e\). The authors construct a family \(\mathcal F^k_0(\rho)\) of \(p\)-ary sequences of period \(p^n-1\) for arbitrary positive integers \(1\leq \rho \leq m\) and \(k\) with \(\gcd(n,k)=e\). They show that, for a given \(\rho\), \(\mathcal F^k_0(\rho )\) has family size \(p^{n\rho}\), maximum correlation \(1 + p^{\frac{n+(2\rho -1)e}{2}}\), and maximum linear span \((m+1)n\).