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Some Remarks on BCH Bounds and Minimum Weights of Binary Primitive BCH Codes
IEEE Transactions on Information Theory, 1969It is shown that if m \neq 8, 12 and m > 6 , there are some binary primitive BCH codes (BCH codes in a narrow sense) of length 2^{m} - 1 whose minimum weight is greater than the BCH bound. This gives a negative answer to the question posed by Peterson [1] of whether or not the BCH bound is always the actual minimum weight of a binary primitive BCH code.
Kasami, Tadao, Tokura, Nobuki
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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.
H. Helgert, R. Stinaff
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2021
Tämän tutkielman tarkoituksena on tutustuttaa lukija BCH-koodeihin. BCH-koodit ovat syklisiä koodeja ja ne pystyvät korjaamaan useita virheitä. Tutkielmassa esitetään erilaisia tapoja korjata koodisanoihin tulleita virheitä käyttäen hyväksi äärellisten kuntien teoriaa ja lineaari- sekä polynomialgebraa.
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Tämän tutkielman tarkoituksena on tutustuttaa lukija BCH-koodeihin. BCH-koodit ovat syklisiä koodeja ja ne pystyvät korjaamaan useita virheitä. Tutkielmassa esitetään erilaisia tapoja korjata koodisanoihin tulleita virheitä käyttäen hyväksi äärellisten kuntien teoriaa ja lineaari- sekä polynomialgebraa.
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2020
Bislang haben wir uns nur die Linearitat zunutze gemacht und noch keine fortgeschritteneren Methoden der Algebra verwendet. Rechnen mit Matrizen ist fur praktische Zwecke aber zu komplex. Wesentlich einfacher ist das Rechnen mit Polynomen, die auch in fruheren Kapiteln bereits eine wichtige Rolle gespielt haben.
Gisbert Wüstholz, Clemens Fuchs
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Bislang haben wir uns nur die Linearitat zunutze gemacht und noch keine fortgeschritteneren Methoden der Algebra verwendet. Rechnen mit Matrizen ist fur praktische Zwecke aber zu komplex. Wesentlich einfacher ist das Rechnen mit Polynomen, die auch in fruheren Kapiteln bereits eine wichtige Rolle gespielt haben.
Gisbert Wüstholz, Clemens Fuchs
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2008 International Conference on Computer Engineering & Systems, 2008
Recently, the theory of quantum error control codes has been extended to include quantum codes over asymmetric quantum channels - qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in constructing quantum error control codes has focused on code constructions for symmetric quantum channels.
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Recently, the theory of quantum error control codes has been extended to include quantum codes over asymmetric quantum channels - qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in constructing quantum error control codes has focused on code constructions for symmetric quantum channels.
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2018
The theory of error-correcting codes is a key pillar in modern digital communications. By introducing redundancy into codewords, error-correcting codes make messages robust against noises in communication channels. In 1948, Shannon proved that arbitrarily reliable communications are possible with the help of error-correcting codes.
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The theory of error-correcting codes is a key pillar in modern digital communications. By introducing redundancy into codewords, error-correcting codes make messages robust against noises in communication channels. In 1948, Shannon proved that arbitrarily reliable communications are possible with the help of error-correcting codes.
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European Journal of Nuclear Medicine and Molecular Imaging, 2023
Guohong Song, Hua Zhu, Zhi Yang
exaly
Guohong Song, Hua Zhu, Zhi Yang
exaly