Evaluation of cross-correlation values of p-ary m-sequence and its decimated sequence by pn+1 over p+1 + pn−1 over 2

For a prime p ≡ 1 mod 4, an odd integer n, and d = p
ⁿ
+1/p+1 + p
ⁿ
-1/2, we investigate the cross-correlation values of p-ary m-sequence m(t) of period p
ⁿ
- 1 and its decimated m-sequence m(dt). It is shown that the cross-correlation function between m(t) and m(dt) takes the values in {-1, -1 ± p
^n/2
, -1 ± 1+√p/2 p
^n/2
, -1 ± p-1/2 p
^n/2
}.