<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>De Bruijn sequence is an important kind of nonlinear shift register sequence, which has a very wide range of applications in the fields of communication and cryptography. From the perspective of the relationship between linear terms, quadratic terms and cubic terms in the feedback functions of de Bruijn sequences, some new necessary conditions for feedback functions of de Bruijn sequences are obtained. Some examples show that the known necessary conditions cannot deduce the proposed necessary conditions.</p>
</abstract>

De Bruijn sequence is an important kind of nonlinear shift register sequence, which has a very wide range of applications in the fields of communication and cryptography. From the perspective of the relationship between linear terms, quadratic terms and cubic terms in the feedback functions of de Bruijn sequences, some new necessary conditions for feedback functions of de Bruijn sequences are obtained. Some examples show that the known necessary conditions cannot deduce the proposed necessary conditions.

Some necessary conditions for feedback functions of de Bruijn sequences

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Some necessary conditions for feedback functions of de Bruijn sequences"}

De Bruijn sequence is an important kind of nonlinear shift register sequence, which has a very wide range of applications in the fields of communication and...

Some necessary conditions for feedback functions of de Bruijn sequences

Published Online: Dec 23, 2022

Page range: 215 - 224

Received: Jun 14, 2022

Accepted: Aug 30, 2022

DOI: https://doi.org/10.2478/amns.2021.2.00305

Keywords
linear feedback shift register, nonlinear feedback shift register, de Bruijn sequence, feedback function, Boolean function, algebraic normal form, nonlinear term

© 2023 Daohuan Hu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Some necessary conditions for feedback functions of de Bruijn sequences

Published Online: Dec 23, 2022

Page range: 215 - 224

Received: Jun 14, 2022

Accepted: Aug 30, 2022

DOI: https://doi.org/10.2478/amns.2021.2.00305

Keywordslinear feedback shift register, nonlinear feedback shift register, de Bruijn sequence, feedback function, Boolean function, algebraic normal form, nonlinear term

© 2023 Daohuan Hu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
linear feedback shift register, nonlinear feedback shift register, de Bruijn sequence, feedback function, Boolean function, algebraic normal form, nonlinear term