On the linear complexity for multidimensional sequences

TL;DR

This paper extends the concept of linear complexity to multidimensional sequences over finite fields, providing probabilistic bounds for their linear and $k$-error linear complexities, which are crucial for sequence analysis and cryptography.

Contribution

It introduces a generalized definition of linear complexity for multidimensional sequences and establishes probabilistic bounds for their complexity measures.

Findings

Derived lower and upper bounds for linear complexity

Established bounds for $k$-error linear complexity

Probabilistic validity of the bounds

Abstract

In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and $k$-error linear complexity of multidimensional periodic sequences.