Abstract: Let p be an odd prime and n≥3, and k be positive integers with gcd(k,n)=1. Utilizing a class of quadratic forms over Fpn, a new family of p-ary sequences with period pn－1 was proposed. The proposed family has family size p2n and maximum correlation pn/2+1+1. The correlation distribution of the family was completely determined. Compared with the known sequence families, the proposed family has larger family size, while still maintaining low correlation.

Key words: quadratic form, exponential sum, p-ary sequences, finite fields