Open Access

ARTICLE

Quaternion Integers Based Higher Length Cyclic Codes and Their Decoding Algorithm

Muhammad Sajjad¹, Tariq Shah^1,*, Mohammad Mazyad Hazzazi², Adel R. Alharbi³, Iqtadar Hussain⁴

1 Department of Mathematics, Quaid-I-Azam University, Islamabad, 45320, Pakistan
2 Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia
3 College of Computing and Information Technology, University of Tabuk, Tabuk, 71491, Saudi Arabia
4 Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, Qatar

* Corresponding Author: Tariq Shah. Email:

Computers, Materials & Continua 2022, 73(1), 1177-1194. https://doi.org/10.32604/cmc.2022.025245

Received 17 November 2021; Accepted 15 February 2022; Issue published 18 May 2022

Abstract

The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields. Following these lines, the decoding algorithms for the correction of errors of length cyclic codes over quaternion integers of Quaternion Mannheim weight one up to two coordinates have considered. In continuation, the case of cyclic codes of lengths and has studied to improve the error correction efficiency. In this study, we present the decoding of cyclic codes of length and length 2 (where is prime integer and is Euler phi function) over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors. Furthermore, the error correction capability and code rate tradeoff of these codes are also discussed. Thus, an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.

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Keywords

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