On the linear complexity of binary lattices

Katalin Gyarmati, Christian Mauduit, András Sárközy

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Linear complexity is an important and frequently used measure of unpredictability and pseudorandomness of binary sequences. In this paper our goal is to extend this notion to two dimensions. We will define and study the linear complexity of binary lattices. The linear complexity of a truly random binary lattice will be estimated. Finally, we will analyze the connection between linear complexity and correlation measures, and we will utilize the inequalities obtained in this way for estimating the linear complexity of an important special binary lattice. Finally, we will study the connection between the linear complexity of binary lattices and of the associated binary sequences.

Original languageEnglish
Pages (from-to)185-201
Number of pages17
JournalRamanujan Journal
Volume32
Issue number2
DOIs
Publication statusPublished - Nov 1 2013

Keywords

  • Binary lattice
  • Linear complexity
  • Linear recursion
  • Pseudorandomness
  • Two dimensions

ASJC Scopus subject areas

  • Algebra and Number Theory

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