Analysis and Computation of Multidimensional Linear Complexity of Periodic Arrays

Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional linear complexity of periodic arrays obtained using the defi...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-07
Main Authors: Arce, Rafael, Hernández, Carlos, Ortiz, José, Rubio, Ivelisse, Torres, Jaziel
Format: Article
Language:English
Subjects:
Arrays
Asymptotic methods
Asymptotic properties
Complexity
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional linear complexity of periodic arrays obtained using the definition and method proposed in \cite{ArCaGoMoOrRuTi,GoHoMoRu,MoHoRu}. The results include a generalization of a bound for the linear complexity, a comparison with the measure of complexity for multisequences, and computations of the complexity of arrays with periods that are not relatively prime for which the ``unfolding method'' does not work. Conjectures for exact formulas and the asymptotic behavior of the complexity of some array constructions are formulated. We also present open source software for constructing multidimensional arrays and for computing their multidimensional linear complexity.
ISSN:2331-8422