On the Cross-Correlation of a $p$-Ary ${m}$-Sequence of Period $p^{2m}-1$ and Its Decimated Sequences by $ {{ (p^{m}+1)^{2}}/ { 2(p+1)}}$

Abstract

In this paper, for an odd prime , we investigate into the cross-correlation of a p-ary m-sequence m(t) of period p ;n ;-1 and its d-decimated sequences m(dt+l), 0≤l ;m ;+1)/2, where d=(pm+1)2/2(p+l), n=2m, and m is an odd integer. There are (pm+1)/2 distinct decimated sequences m(dt+l) since gcd(d,pn-1)=(pm+1)/2. It is shown that the magnitude of the cross-correlation values is upper bounded by (p+1)/2 pn/2+1 . We also construct the sequence family F from these sequences, where the family size is pm and the correlation magnitude is upper bounded by (pm+1)/2 pn/2+1.