Some new three-valued crosscorrelation functions for binary m-sequences

Thomas W. Cusick; Hans Dobbertin

doi:10.1109/18.508848

Some new three-valued crosscorrelation functions for binary m-sequences

Thomas W. Cusick
, Hans Dobbertin

Mathematics

University at Buffalo

German Information Security Agency

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

In 1972 Niho gave various conjectures about the crosscorrelation between a binary maximum-length linear shift register sequence and a decimation of that sequence by an integer d. We prove that the crosscorrelation function for two new values of d takes on precisely three values and thereby confirm two of Niho's conjectures.

Original language	English
Pages (from-to)	1238-1240
Number of pages	3
Journal	IEEE Transactions on Information Theory
Volume	42
Issue number	4
DOIs	https://doi.org/10.1109/18.508848
State	Published - 1996

Keywords

Crosscorrelation
Finite fields
Linear recursions
Niho conjectures
Walsh transform
m-sequences

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title = "Some new three-valued crosscorrelation functions for binary m-sequences",

abstract = "In 1972 Niho gave various conjectures about the crosscorrelation between a binary maximum-length linear shift register sequence and a decimation of that sequence by an integer d. We prove that the crosscorrelation function for two new values of d takes on precisely three values and thereby confirm two of Niho's conjectures.",

keywords = "Crosscorrelation, Finite fields, Linear recursions, Niho conjectures, Walsh transform, m-sequences",

author = "Cusick, \{Thomas W.\} and Hans Dobbertin",

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AU - Dobbertin, Hans

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AB - In 1972 Niho gave various conjectures about the crosscorrelation between a binary maximum-length linear shift register sequence and a decimation of that sequence by an integer d. We prove that the crosscorrelation function for two new values of d takes on precisely three values and thereby confirm two of Niho's conjectures.

KW - Crosscorrelation

KW - Finite fields

KW - Linear recursions

KW - Niho conjectures

KW - Walsh transform

KW - m-sequences

UR - https://www.scopus.com/pages/publications/0030190485

U2 - 10.1109/18.508848

DO - 10.1109/18.508848

M3 - Article

SN - 0018-9448

VL - 42

SP - 1238

EP - 1240

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 4

ER -

Some new three-valued crosscorrelation functions for binary m-sequences

Abstract

Keywords

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