Cross-Correlation Distribution of $p$ -ary $m$ -Sequence of Period

For an odd prime p, n=4k, and d=((p^2k+1)/2)², there are (p^2k+1)/2 distinct decimated sequences s(dt+l), 0lesl<(p^2k+)/2,of a p-ary m-sequence s(t) of period pⁿ-1 because gcd(d,pⁿ-1)=(p^2k+1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l),0lesl<(p^2k+1)/2, takes the values in {-1, -1 -radic(pⁿ),-1+radic(pⁿ),-1+2radic(pⁿ)} and their cross-correlation distribution is also derived.