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

<p>In this paper, we introduce a <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_candc-2021-0017_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>Q</mi></mrow><mn>2</mn><mi>n</mi></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>
<tex-math>Q_2^n\left( x \right)</tex-math>
</alternatives>
</inline-formula> matrix, whose elements are balancing polynomials, and develop a new coding and decoding method following from the <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_candc-2021-0017_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>Q</mi></mrow><mn>2</mn><mi>n</mi></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>
<tex-math>Q_2^n\left( x \right)</tex-math>
</alternatives>
</inline-formula> matrix. We establish the relations between the code matrix elements, error detection and correction for this coding theory.</p>
</abstract>

In this paper, we introduce a 


Q2n(x)
Q_2^n\left( x \right)

 matrix, whose elements are balancing polynomials, and develop a new coding and decoding method following from the 


Q2n(x)
Q_2^n\left( x \right)

 matrix. We establish the relations between the code matrix elements, error detection and correction for this coding theory.

Coding theory based on balancing polynomials

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Coding theory based on balancing polynomials"}

In this paper, we introduce a 


Q2n(x)
Q_2^n\left( x \right)

 matrix, whose elements are balancing polynomials, and develop a new coding and decoding method...

Coding theory based on balancing polynomials

Published Online: Jun 28, 2022

Page range: 335 - 346

Received: Jan 01, 2020

Accepted: Jan 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0017

Keywords
balancing numbers, -balancing numbers, balancing polynomials

© 2021 Bandhu Prasad, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Coding theory based on balancing polynomials

Published Online: Jun 28, 2022

Page range: 335 - 346

Received: Jan 01, 2020

Accepted: Jan 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0017

Keywordsbalancing numbers, -balancing numbers, balancing polynomials

© 2021 Bandhu Prasad, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
balancing numbers, -balancing numbers, balancing polynomials