New Families of p-Ary Sequences of Period $ rac{p^n-1}{2}$ with Low Maximum Correlation Magnitude

Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd integer. In this paper, two new families of p-ary sequences of period N = p −1 2 are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d = 4 and d = (p +1)/2 = N +1. The upper bound on the magnitude of correlation values of two sequences in the family is derived using Weil bound. Their upper bound is derived as 3 √ 2 √ N + 12 + 1 2 and the family size is 4N , which is four times the period of the sequence.