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Narrow-Sense BCH Codes Over $ {\mathrm {GF}}(q)$ With Length $n=\frac {q^{m}-1}{q-1}$
- Source :
- IEEE Transactions on Information Theory. 63:7219-7236
- Publication Year :
- 2017
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2017.
-
Abstract
- Cyclic codes are widely employed in communication systems, storage devices, and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. A subclass of good BCH codes are the narrow-sense BCH codes over $ {\mathrm {GF}}(q)$ with length $n=(q^{m}-1)/(q-1)$ . Little is known about this class of BCH codes when $q>2$ . The objective of this paper is to study some of the codes within this class. In particular, the dimension, the minimum distance, and the weight distribution of some ternary BCH codes with length $n=(3^{m}-1)/2$ are determined in this paper. A class of ternary BCH codes meeting the Griesmer bound is identified. An application of some of the BCH codes in secret sharing is also investigated.
- Subjects :
- Discrete mathematics
Minimum distance
Dimension (graph theory)
020206 networking & telecommunications
0102 computer and information sciences
02 engineering and technology
Sense (electronics)
Library and Information Sciences
01 natural sciences
Electronic mail
Computer Science Applications
010201 computation theory & mathematics
Weight distribution
0202 electrical engineering, electronic engineering, information engineering
Ternary operation
BCH code
Decoding methods
Information Systems
Mathematics
Subjects
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 63
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi...........926345157a2eee9f18964481b6c9f26c