On decimations of ℓ-sequences

Mark Goresky; Andrew Klapper; Ram Murty; Igor Shparlinski

doi:10.1137/S0895480102403428

On decimations of ℓ-sequences

Mark Goresky^*, Andrew Klapper, Ram Murty, Igor Shparlinski

^*Corresponding author for this work

School of Computing

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

19 Citations (Scopus)

Abstract

Maximal length feedback with carry shift register sequences have several remarkable statistical properties. Among them is the property that the arithmetic correlations between any two cyclically distinct decimations are precisely zero. It is open, however, whether all such pairs of decimations are indeed cyclically distinct. In this paper we show that the set of distinct decimations is large and, in some cases, all decimations are distinct.

Original language	English
Pages (from-to)	130-140
Number of pages	11
Journal	SIAM Journal on Discrete Mathematics
Volume	18
Issue number	1
DOIs	https://doi.org/10.1137/S0895480102403428
Publication status	Published - Jul 2004

Keywords

Arithmetic correlation
Binary sequence
Exponential sum
Feedback with carry shift register
p-adic number

Access to Document

10.1137/S0895480102403428

Cite this

@article{d7db456bfa8642beb311fb05f208f1d4,

title = "On decimations of ℓ-sequences",

abstract = "Maximal length feedback with carry shift register sequences have several remarkable statistical properties. Among them is the property that the arithmetic correlations between any two cyclically distinct decimations are precisely zero. It is open, however, whether all such pairs of decimations are indeed cyclically distinct. In this paper we show that the set of distinct decimations is large and, in some cases, all decimations are distinct.",

keywords = "Arithmetic correlation, Binary sequence, Exponential sum, Feedback with carry shift register, p-adic number",

author = "Mark Goresky and Andrew Klapper and Ram Murty and Igor Shparlinski",

year = "2004",

month = jul,

doi = "10.1137/S0895480102403428",

language = "English",

volume = "18",

pages = "130--140",

journal = "SIAM Journal on Discrete Mathematics",

issn = "0895-4801",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - On decimations of ℓ-sequences

AU - Goresky, Mark

AU - Klapper, Andrew

AU - Murty, Ram

AU - Shparlinski, Igor

PY - 2004/7

Y1 - 2004/7

N2 - Maximal length feedback with carry shift register sequences have several remarkable statistical properties. Among them is the property that the arithmetic correlations between any two cyclically distinct decimations are precisely zero. It is open, however, whether all such pairs of decimations are indeed cyclically distinct. In this paper we show that the set of distinct decimations is large and, in some cases, all decimations are distinct.

AB - Maximal length feedback with carry shift register sequences have several remarkable statistical properties. Among them is the property that the arithmetic correlations between any two cyclically distinct decimations are precisely zero. It is open, however, whether all such pairs of decimations are indeed cyclically distinct. In this paper we show that the set of distinct decimations is large and, in some cases, all decimations are distinct.

KW - Arithmetic correlation

KW - Binary sequence

KW - Exponential sum

KW - Feedback with carry shift register

KW - p-adic number

UR - http://www.scopus.com/inward/record.url?scp=14644420858&partnerID=8YFLogxK

U2 - 10.1137/S0895480102403428

DO - 10.1137/S0895480102403428

M3 - Article

AN - SCOPUS:14644420858

SN - 0895-4801

VL - 18

SP - 130

EP - 140

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 1

ER -

On decimations of ℓ-sequences

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this