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On codes over quaternion integers.
- Source :
-
Applicable Algebra in Engineering, Communication & Computing . Dec2013, Vol. 24 Issue 6, p477-496. 20p. - Publication Year :
- 2013
-
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 $$n$$ 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 $$n$$ n length cyclic code there exist a cyclic code of length $$2n-1$$ 2 n - 1 . The decoding algorithms for the cyclic code of length $$2n-1$$ 2 n - 1 are given, which correct errors of quaternion Mannheim weight one and two. In addition, we show that the cyclic code of length $$2n-1$$ 2 n - 1 is maximum-distance separable (MDS) with respect to Hamming distance. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 24
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 91993043
- Full Text :
- https://doi.org/10.1007/s00200-013-0203-2