Back to Search
Start Over
BCH Codes for the Rosenbloom–Tsfasman Metric
- Source :
- IEEE Transactions on Information Theory. 62:6757-6767
- Publication Year :
- 2016
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2016.
-
Abstract
- 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.
- Subjects :
- Block code
Discrete mathematics
Berlekamp–Welch algorithm
Reed–Muller code
020206 networking & telecommunications
Data_CODINGANDINFORMATIONTHEORY
0102 computer and information sciences
02 engineering and technology
Library and Information Sciences
01 natural sciences
Linear code
Computer Science Applications
Combinatorics
Computer Science::Discrete Mathematics
010201 computation theory & mathematics
Reed–Solomon error correction
0202 electrical engineering, electronic engineering, information engineering
Tornado code
Hardware_ARITHMETICANDLOGICSTRUCTURES
Folded Reed–Solomon code
BCH code
Computer Science::Information Theory
Information Systems
Mathematics
Subjects
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi...........bf02c34388c01fa7b82d720e615c2ab3