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

Let p be an odd prime and n = ( 2 m + 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 p -ary case. As a result, we obtain a new family F o k ( ρ ) of p -ary sequences of period p n − 1 for arbitrary positive integers 1 ≤ ρ ≤ m and k with gcd ( n , k ) = e . It is shown that, for a given ρ , F o k ( ρ ) has family size p n ρ , maximum correlation 1 + p n + ( 2 ρ − 1 ) e 2 , and maximum linear span ( m + 1 ) n . In particular, the new family F o k ( ρ ) contains Tang, Udaya, and Fan’s construction as a subset, if an m -sequence is excluded.