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

Let pp be an odd prime and n=(2m+1)en=(2m+1)e. Based on the theory of quadratic forms over finite fields of odd characteristic, we generalize the binary construction by Yu and Gong to pp-ary case. As a result, we obtain a new family Fok(ρ) of pp-ary sequences of period pn−1pn−1 for arbitrary positive integers 1≤ρ≤m1≤ρ≤m and kk with gcd(n,k)=egcd(n,k)=e. It is shown that, for a given ρρ, Fok(ρ) has family size pnρpnρ, maximum correlation 1+pn+(2ρ−1)e2, and maximum linear span (m+1)n(m+1)n. In particular, the new family Fok(ρ) contains Tang, Udaya, and Fan’s construction as a subset, if an mm-sequence is excluded.