BCH Codes for the Rosenbloom-Tsfasman Metric

BCH Codes for the Rosenbloom-Tsfasman Metric

The Rosenbloom-Tsfasman metric has attracted the attention of many researchers as a generalization of the Hamming metric that is relevant to practical problems. Codes for this metric were considered. In particular, Reed-Solomon codes were generalized to be compatible with this metric. In this paper,...

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Veröffentlicht in:IEEE transactions on information theory 2016-12, Vol.62 (12), p.6757-6767
Hauptverfasser: Zhou, Wei, Lin, Shu, Abdel-Ghaffar, Khaled A. S.
Format: Artikel
Sprache:eng
Schlagworte:
BCH code
Encoding
Fourier transforms
Galois-Fourier transform
Hamming distance
Hasse derivative
Information theory
Measurement
Media
Reed-Solomon codes
Reed–Solomon code
Reliability
Rosenbloom–Tsfasman metric
Transforms
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Zusammenfassung:The Rosenbloom-Tsfasman metric has attracted the attention of many researchers as a generalization of the Hamming metric that is relevant to practical problems. Codes for this metric were considered. In particular, Reed-Solomon codes were generalized to be compatible with this metric. In this paper, a generalization of BCH codes for the Rosenbloom-Tsfasman metric is proposed. This generalization is based on considering BCH codes as subfield subcodes of Reed-Solomon codes. By characterizing these subfield subcodes, an explicit construction of BCH codes for the Rosenbloom-Tsfasman metric is provided. Two important properties of Reed-Solomon codes and BCH codes for the Rosenbloom-Tsfasman metric are studied and compared with those for the Hamming metric. These properties are cyclic structure and duality. The approach is based on Galois-Fourier transforms associated with Hasse derivatives.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2016.2617312