Results 141 to 150 of about 1,776 (185)

BCH cyclic codes

Discrete Mathematics
BCH codes are a subclass of cyclic codes with many interesting properties. Over the last sixty years, a lot of progress has been made in the study of BCH codes. This survey paper presents the state-of-the-art of BCH cyclic codes and their applications.
Ding Cunsheng, Chengju Li
exaly   +4 more sources

Shortened BCH codes (Corresp.)

IEEE Transactions on Information Theory, 1973
By 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
exaly   +2 more sources

Two Families of LCD BCH Codes

IEEE Transactions on Information Theory, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding Cunsheng, Chengju Li, Shuxing Li
exaly   +4 more sources

On a class of primitive BCH-codes

IEEE Transactions on Information Theory, 1990
The author introduces a special class of primitive BCH codes, the minimal BCH (MB) codes. It is proved that an MB code has as minimum distance its designed distance. Using the Roos bound, the author proposes a lower bound, sometimes tight, for the minimum distance of the dual of an MB code.
exaly   +2 more sources

On generalized Hamming weights of BCH codes

IEEE Transactions on Information Theory, 1994
A method is introduced to determine the generalized Hamming weights [\textit{V. K. Wei}, IEEE Trans. Inf. Theory 37, No. 5, 1412--1418 (1991; Zbl 0735.94008)] of certain families of codes, by the use of a geometric description of their dual. This method is ruled out by the authors to calculate some generalized weights of BCH(2) and BCH(3).
M Van Der Vlugt
exaly   +5 more sources

On classical BCH codes and quantum BCH codes

Journal of Electronics (China), 2009
It 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
openaire   +1 more source

On spectra of BCH codes

Eighteenth Convention of Electrical and Electronics Engineers in Israel, 1995
The authors give asymptotically better estimates for the error term in the binomial approximation of spectra of BCH codes than the ones derived by Sidelnikov, Kasami-Fujikawa-Lin and Solé.
Ilia Krasikov, Simon Litsyn
openaire   +1 more source

The Dual Codes of Several Classes of BCH Codes

IEEE Transactions on Information Theory, 2022
As a special subclass of cyclic codes, BCH codes have wide applications in communication and storage systems. A BCH code of length n over Fq is always relative to an n-th primitive root of unity β in an extension field of Fq, and is called a dually-BCH code if its dual is also a BCH code relative to the same β.
Binkai Gong, Cunsheng Ding, Chengju Li
openaire   +2 more sources

On decoding BCH codes

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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Some negacyclic BCH codes and quantum codes

Quantum Information Processing, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junli Wang 0002, Ruihu Li, Yang Liu 0035, Guanmin Guo   +3 more
openaire   +2 more sources