The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Laisser nous d=2pm-1 soit la décimation Niho sur $mathbb{F}_{p^{2m}}$ satisfaisant $gcd(d,p^{2m}-1)=3$, où m est un entier positif impair et p est un premier avec p ≡ 2(mod 3). La fonction de corrélation croisée entre les p-aire m- séquence de période p2m-1 et c'est tout d-une séquence de décimation avec une courte période $ rac{p^{2m}-1}{3}$ est étudiée. Il est prouvé que pour chaque d-séquence de décimation, la fonction de corrélation croisée prend quatre valeurs et la distribution de corrélation correspondante est complètement déterminée. Ceci étend les résultats de Niho et Helleseth pour le cas pgcd(d, p2m-1)=1.
Yongbo XIA
South-Central University for Nationalities
Shiyuan HE
South-Central University for Nationalities
Shaoping CHEN
South-Central University for Nationalities
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Yongbo XIA, Shiyuan HE, Shaoping CHEN, "Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 2, pp. 450-457, February 2019, doi: 10.1587/transfun.E102.A.450.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.450/_p
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@ARTICLE{e102-a_2_450,
author={Yongbo XIA, Shiyuan HE, Shaoping CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period},
year={2019},
volume={E102-A},
number={2},
pages={450-457},
abstract={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.},
keywords={},
doi={10.1587/transfun.E102.A.450},
ISSN={1745-1337},
month={February},}
Copier
TY - JOUR
TI - Correlation Distributions between an m-Sequence and Its Niho Decimation Sequences of Short Period
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 450
EP - 457
AU - Yongbo XIA
AU - Shiyuan HE
AU - Shaoping CHEN
PY - 2019
DO - 10.1587/transfun.E102.A.450
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2019
AB - 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.
ER -