A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences
Information Theory
2022-02-04 v1 math.IT
Abstract
A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique least-degree characteristic polynomial. Leveraging on a recent characterization, we devise a novel general approach to determine the minimal polynomial. We translate the characterization into a problem of identifying a Hamiltonian cycle in a specially constructed graph. Along the way, we demonstrate the usefullness of computational tools from the cycle joining method in the modified setup.
Keywords
Cite
@article{arxiv.2202.01425,
title = {A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences},
author = {Musthofa and Indah Emilia Wijayanti and Diah Junia Eksi Palupi and Martianus Frederic Ezerman},
journal= {arXiv preprint arXiv:2202.01425},
year = {2022}
}