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Journal of the Belarusian State University. Mathematics and Informatics, 2020, Volume 2, Pages 36–48
DOI: https://doi.org/10.33581/2520-6508-2020-2-36-48 (Mi bgumi48) 		 
Mathematical logic, Algebra and Number Theory

Generic BCH codes. Polynomial-norm error decoding

A. V. Kushnerova, V. A. Lipnitskiba

a Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
b Military Academy of the Republic of Belarus, 220 Niezaliežnasci Avenue, Minsk 220057, Belarus
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DOI: https://doi.org/10.33581/2520-6508-2020-2-36-48
Abstract: The classic Bose – Chaudhuri – Hocquenghem (BCH) codes is famous and well-studied part in the theory of error-correcting codes. Generalization of BCH codes allows us to expand the range of activities in the practical correction of errors. Some generic BCH codes are able to correct more errors than classic BCH code in one message block. So it is important to provide appropriate method of error correction. After our investigation it was found that polynomial-norm method is most convenient and effective for that task. The result of the study was a model of a polynomial-norm decoder for a generic BCH code at length 65.
Keywords: error correcting codes; Bose – Chaudhuri – Hocquenghem codes; automorphisms of codes; norm decoding method; polynomial-norm decoding method.
Received: 29.01.2020
Document Type: Article
UDC: 519.725
Language: Russian
Citation: A. V. Kushnerov, V. A. Lipnitski, “Generic BCH codes. Polynomial-norm error decoding”, Journal of the Belarusian State University. Mathematics and Informatics, 2 (2020), 36–48
Citation in format AMSBIB
\Bibitem{KusLip20}
\by A.~V.~Kushnerov, V.~A.~Lipnitski
\paper Generic BCH codes. Polynomial-norm error decoding
\jour Journal of the Belarusian State University. Mathematics and Informatics
\yr 2020
\vol 2
\pages 36--48
\mathnet{http://mi.mathnet.ru/bgumi48}
\crossref{https://doi.org/10.33581/2520-6508-2020-2-36-48}
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