Quaternion Integers Based Higher Length Cyclic Codes and Their Decoding Algorithm  

作　　者：Muhammad Sajjad Tariq Shah Mohammad Mazyad Hazzazi Adel R.Alharbi Iqtadar Hussain 

机构地区：[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

出　　处：《Computers, Materials & Continua》2022年第10期1177-1194,共18页计算机、材料和连续体（英文）

基　　金：The authors extend their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P.1/85/42.

摘　　要：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 n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis 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.

关 键 词：Mannheim distance monoid ring cyclic codes parity check matrix extension syndromes decoding code rate and error correction capability 

分 类 号：O15[理学—数学]