On Four-Valued Niho-Type Cross-Correlation Functions of $m$ -Sequences

Consider the cross-correlation function C_d(tau) between two m-sequences of period p^2k-1 that differ by a decimation d. Assume that d is of Niho type and C_d(tau) is four-valued. In this correspondence, the values of C_d(tau) are described. If p=2 then the values of C_d(tau) are -1-2 ^k,-1,-1+2^k, and -1+2^k+j for some integer j>0 for which 2j divides k. If p>2 then the values are -1-p^k,-1,-1+p^k, and -1+2middotp^k