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On the linear complexity of binary lattices |
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| Authors: | Katalin Gyarmati Christian Mauduit András Sárközy |
| Affiliation: | 1. Department of Algebra and Number Theory, E?tv?s Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary 2. Institut de Mathématiques de Luminy, CNRS, FRE 3529, Université Aix-Marseille, 163 avenue de Luminy, 13288, Marseille Cedex 9, France 3. Instituto de Matemática Pura e Aplicada, IMPA-CNRS, UMI 2924, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil |
| 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. |
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