Further Results on $m$-Sequences With Five-Valued Cross Correlation
Aina Johansen, Tor Helleseth, Alexander Kholosha · IEEE Transactions on Information Theory · 2009
Recently, the complete five-valued cross-correlation distribution has been determined between twom-sequences{st} and{sdt} of periods2m-1 that differ by the decimationd= [(22k+1)/(2k+1)] wheremis odd andk= 1, i.e.,d= 5/3 . In this paper, the correlation distribution is given in terms of some exponential sums for anykwhengcd(k,m) = 1 andmis odd. Furthermore, two new conjectures on exponential sums are presented that are of interest in their own right. Proving these conjectures would imply that the correlation distribution is independent ofkunder the conditions above and thus the same as for the casek= 1. The conjectures are proven formodd andk= 2 and the paper gives a new result that the correlation distribution ford=17/5 is the same as ford= 5/3.