On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated hi Sequences by d = pn+1/Pk+1+pn-1/2

In this paper, for an odd prime p such that p 3 mod 4, odd n, and d = (p(n) + 1)/(p(k) + 1)+ (p(n) - 1)/2 with k vertical bar n, the value distribution of the exponential sum S (a, b) is calculated as a and b run through F-pn. The sequence family G in which each sequence has the period of N = p(n) - 1 is also constructed. The family size of G is p(n) and the correlation magnitude is roughly upper bounded by (p(k) + 1) root N/2. The weight distribution of the relevant cyclic code C over F-p with the length N and the dimension dimF(p) C = 2n is also derived.