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