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      Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences

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          Abstract

          Motivated by the known autocorrelation properties of the Rudin-Shapiro sequence, we study the discrete correlation among infinite sequences over a finite alphabet, where we just take into account whether two symbols are identical. We show by combinatorial means that sequences cannot be "too" different, and by an explicit construction generalizing the Rudin-Shapiro sequence, we show that we can achieve the maximum possible difference.

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          Author and article information

          Journal
          2008-12-16
          2009-02-11
          Article
          0812.3186
          cb616708-311b-4b31-8ad3-4acbf6e80017

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          68R15; 11K38; 11A63; 05D99; 11K31
          Improved Introduction and new Section 6 (Lovasz local lemma)
          math.CO cs.FL math.NT

          Theoretical computer science,Combinatorics,Number theory
          Theoretical computer science, Combinatorics, Number theory

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