Measures of pseudorandomness for finite sequences: Minimal values

N. Alon, Y. Kohayakawa, C. Mauduit, C. G. Moreira, V. Rödl

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

Mauduit and Sárközy introduced and studied certain numerical parameters associated to finite binary sequences EN ∈ {-1,1}N in order to measure their 'level of randomness'. Two of these parameters are the normality measure N(EN)$ and the correlation measure $C_k(E_N)$ of order k, which focus on different combinatorial aspects of $E_N$. In their work, amongst others, Mauduit and Sárközy investigated the minimal possible value of these parameters. In this paper, we continue the work in this direction and prove a lower bound for the correlation measure $C_k(E_N)$ (k even) for arbitrary sequences $E_N$, establishing one of their conjectures. We also give an algebraic construction for a sequence $E_N$ with small normality measure N(EN).

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalCombinatorics Probability and Computing
Volume15
Issue number1-2
DOIs
StatePublished - Jan 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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