Name
Abstract | ||
|---|---|---|
Abstract Decoding algorithms for the correction of errors for cyclic codes over quaternion integers of quaternion Mannheim weight one up to two coordinates are discussed by Özen and Güzeltepe (Eur J Pure Appl Math 3(4):670–677, 2010). Though, Neto et al. (IEEE Trans Inf Theory 47(4):1514–1527, 2001) proposed decoding algorithms for the correction of errors of arbitrary Mannheim weight. In this study, we followed the procedures used by Neto et al. and suggest a decoding algorithm for an \(n\) length cyclic code over quaternion integers to correct errors of quaternion Mannheim weight two up to two coordinates. Furthermore, we establish that; over quaternion integers, for a given \(n\) length cyclic code there exist a cyclic code of length \(2n-1\). The decoding algorithms for the cyclic code of length \(2n-1\) are given, which correct errors of quaternion Mannheim weight one and two. In addition, we show that the cyclic code of length \(2n-1\) is maximum-distance separable (MDS) with respect to Hamming distance. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s00200-013-0203-2 | Appl. Algebra Eng. Commun. Comput. |
Keywords | Field | DocType |
Monoid ring,Cyclic code,Hamming distance,Mannheim distance,Syndrome decoding | Integer,Discrete mathematics,Combinatorics,Monoid ring,Quaternion,Cyclic code,Separable space,Hamming distance,Decoding methods,Hurwitz quaternion,Mathematics | Journal |
Volume | Issue | ISSN |
24 | 6 | 1432-0622 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tariq Shah | 1 | 1 | 2.42 |
| Summera Said Rasool | 2 | 0 | 0.34 |