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

8 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

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KW - Exponential sum

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KW - p-adic number

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On decimations of ℓ-sequences

Abstract

Keywords

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