Cross-Correlation Distribution of p-ary m-Sequence of Period p4k - 1 and Its Decimated Sequences by (p2k+1/2)2

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+1)/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+I), 0lesl< (p^2k+1)/2, takes the values in {-1, -1 - radicpⁿ, -1+radicpⁿ-1+2radicpⁿ} and their cross-correlation distribution is also derived.