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Narrow-Sense BCH Codes Over \mathrm GF(q) With Length n=\frac q^m-1q-1.
- Source :
- IEEE Transactions on Information Theory; Nov2017, Vol. 63 Issue 11, p7219-7236, 18p
- Publication Year :
- 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. [ABSTRACT FROM PUBLISHER]
- Subjects :
- CYCLIC codes
QUADRATIC forms
BCH codes
DECODING algorithms
TELECOMMUNICATION systems
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 63
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 125813361
- Full Text :
- https://doi.org/10.1109/TIT.2017.2743687