On decimations of ℓ-sequences

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


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 languageEnglish
Pages (from-to)130-140
Number of pages11
JournalSIAM Journal on Discrete Mathematics
Issue number1
Publication statusPublished - Jul 2004


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


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