**Elahe Mehraban and Mansour Hashemi**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 29, 2023, Number 3, Pages 503–524

DOI: 10.7546/nntdm.2023.29.3.503-524

**Full paper (PDF, 278 Kb)**

## Details

### Authors and affiliations

Elahe Mehraban

*Department of Mathematics, Near East University TRNC
Mersin 10, Nicosia, 99138, Turkey
*

Mansour Hashemi

*Department of Pure Mathematics, Faculty of Mathematical Sciences,
University of Guilan, Rasht, Iran
*

### Abstract

In this paper, we introduce the generalized balancing sequence and its matrix. Then by using the generalized balancing matrix, we give a coding and decoding method.

### Keywords

- Generalized balancing number
- Coding and decoding method
- Error correction

### 2020 Mathematics Subject Classification

- 68P30
- 11B39
- 11C20

### References

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### Manuscript history

- Received: 16 October 2022
- Revised: 20 April 2023
- Accepted: 18 July 2023
- Online First: 20 July 2023

### Copyright information

Ⓒ 2023 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

## Related papers

- Özkoç, A., & Tekcan, A. (2017). On
*k*-balancing numbers.*Notes on Number Theory and Discrete Mathematics*, 23(3), 38–52. - Shannon, A. G., Erdağ, Ö., & Deveci, Ö. (2021). On the connections between Pell numbers and Fibonacci
*p*-numbers.*Notes on Number Theory and Discrete Mathematics*, 21(1), 148–160.

## Cite this paper

Mehraban, E., & Hashemi, M. (2023). Coding theory on the generalized balancing sequence. *Notes on Number Theory and Discrete Mathematics*, 29(3), 503-524, DOI: 10.7546/nntdm.2023.29.3.503-524.