TY  - EJOU
AU  - Sajjad, Muhammad 
AU  - Shah, Tariq 
AU  - Hazzazi, Mohammad Mazyad 
AU  - Alharbi, Adel R. 
AU  - Hussain, Iqtadar 

TI  - Quaternion Integers Based Higher Length Cyclic Codes and Their Decoding Algorithm
T2  - Computers, Materials \& Continua

PY  - 2022
VL  - 73
IS  - 1
SN  - 1546-2226

AB  - 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.
KW  - Mannheim distance; monoid ring; cyclic codes; parity check matrix extension; syndromes decoding; code rate and error correction capability

DO  - 10.32604/cmc.2022.025245