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

Yongbo XIA  Shiyuan HE  Shaoping CHEN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.2   pp.450-457
Publication Date: 2019/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.450
Type of Manuscript: PAPER
Category: Information Theory
m-sequence,  decimation sequence,  Niho decimation,  cross-correlation function,  correlation distribution,  

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Let d=2pm-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 p2m-1 and its every d-decimation sequence with short period $ rac{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, p2m-1)=1.