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,Dong-Joon Shin,Young-Sik Kim,Jong-Seon No

doi:10.1109/tit.2008.924694

Abstract

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 p n -1 because gcd(d,p n -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(p n ),-1+radic(p n ),-1+2radic(p n )} and their cross-correlation distribution is also derived.

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