<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

Data publikacji: 28 cze 2022

Zakres stron: 335 - 346

Otrzymano: 01 sty 2020

Przyjęty: 01 sty 2021

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

Słowa kluczowe
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

Data publikacji: 28 cze 2022

Zakres stron: 335 - 346

Otrzymano: 01 sty 2020

Przyjęty: 01 sty 2021

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

Słowa kluczowebalancing 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.

Słowa kluczowe
balancing numbers, -balancing numbers, balancing polynomials