Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period

抄録

Let d=2p^m-1 be the Niho decimation over $\mathbb{F}_{p^{2m}}$ satisfying $\gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p^2m-1 and its every d-decimation sequence with short period $\frac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p^2m-1)=1.