Binary Niho sequences with four-valued cross correlations

Let m be odd and q = 2^2m. Let 5r ≡ 1 (mod 2^m + 1) and d = (2^m - 1)r + 1. In this paper, the cross correlation distributions of an m-sequences with period q - 1 and its decimated sequences s(dt + l) with period (q - 1)/3 for 0 ≤ l ≤ 2 are determined. These cross correlations are shown to be four-valued with maximal magnitude 2√q - 1.