Cross-Correlation Distribution of $p$-ary $m$-Sequence of Period $p^{4k}-1$ and Its Decimated Sequences by $\left({{ p^{2k}+1}\over { 2}}\right)^{2}$
Eun-Young Seo, Young Sik Kim, Jong‐Seon No, Dong‐Joon Shin · IEEE Transactions on Information Theory · 2008
For an odd prime p, n=4k, and d=((p2k+1)/2)2, there are (p2k+1)/2 distinct decimated sequences s(dt+l), 0lesl2k+)/2,of a p-ary m-sequence s(t) of period pn-1 because gcd(d,pn-1)=(p2k+1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l),0lesl2k+1)/2, takes the values in {-1, -1 -radic(pn),-1+radic(pn),-1+2radic(pn)} and their cross-correlation distribution is also derived.