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Discrete MathematicsBCH codes are a subclass of cyclic codes with many interesting properties. In many cases BCH codes are the best linear codes. For example, among all binary cyclic codes of odd length n with n≤125 the best cyclic code is always a BCH code except for two ...
Cunsheng Ding, Chengju Li
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On classical BCH codes and quantum BCH codes
Journal of Electronics (China), 2009It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal ...
Yajie Xu, Zhi Ma, Chunyuan Zhang
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Idempotents and the BCH bound [PDF]
IEEE Transactions on Information Theory, 1994 Summary: Using a characterization of the idempotents of a narrow-sense primitive binary BCH code, we are able to give classes of such codes whose minimum distance does not exceed the BCH bound. Our results are compiled in a table.
Augot, Daniel, Sendrier, Nicolas
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IEEE Transactions on Information Theory, 1965
The Gorenstein-Zierler decoding algorithm for BCH codes is extended, modified, and analyzed; in particular, we show how to correct erasures as well as errors, exhibit improved procedures for finding error and erasure values, and consider in some detail the implementation of these procedures in a special-purpose computer.
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The Gorenstein-Zierler decoding algorithm for BCH codes is extended, modified, and analyzed; in particular, we show how to correct erasures as well as errors, exhibit improved procedures for finding error and erasure values, and consider in some detail the implementation of these procedures in a special-purpose computer.
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Mathematics Seminar Notes, 1983
The authors introduce the notion of BCH-algebras as a class of algebras satisfying certain properties of BCI-algebras.
Hu, Qing Ping, Li, Xin
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The authors introduce the notion of BCH-algebras as a class of algebras satisfying certain properties of BCI-algebras.
Hu, Qing Ping, Li, Xin
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Soft BCH-ideals and Idealistic Soft BCH-algebras
2010 International Conference on Artificial Intelligence and Computational Intelligence, 2010Applying soft sets to BCH-algebras, the concepts of soft BCH-ideals and idealistic soft BCH-algebras are introduced, and several examples are given. The intersection, union and “AND” operations of soft BCH-ideals and idealistic soft BCH-algebras are established.
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Shortened BCH codes (Corresp.)
IEEE Transactions on Information Theory, 1973By shortening certain binary primitive BCH codes, we derive a number of linear error-correcting codes with minimum distances superior to any known previously. We also give the weight spectra of three nonprimitive BCH codes whose minimum distances likewise constitute a significant improvement over those of the best codes previously known.
Hermann J. Helgert, Russell D. Stinaff
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