Multisequences with high joint nonlinear complexity

TL;DR

This paper introduces the concept of joint nonlinear complexity for multisequences over finite fields, analyzes specific families, and studies the probabilistic behavior of random multisequences' complexity.

Contribution

It presents a new measure for multisequences, analyzes explicit families, and provides probabilistic insights into the complexity of random multisequences.

Findings

Explicit analysis of joint nonlinear complexity for two multisequence families

Probabilistic results on the behavior of complexity in random multisequences

Introduction of a novel complexity measure for multisequences

Abstract

We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on the behavior of the joint nonlinear complexity of random multisequences over a fixed finite field.