Generic BCH codes. Polynomial-norm error decoding

  • Alexander V. Kushnerov Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-2505-8802
  • Valery A. Lipnitski Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus; Military Academy of the Republic of Belarus, 220 Niezaliežnasci Avenue, Minsk 220057, Belarus
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.

Author Biographies

Alexander V. Kushnerov, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

senior lecturer at the department of differential equations and system analysis, faculty of mechanics  and mathematics

Valery A. Lipnitski, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus; Military Academy of the Republic of Belarus, 220 Niezaliežnasci Avenue, Minsk 220057, Belarus

doctor of science (engineering), full professor; head of the department of higher mathematics, Military Academy of the Republic of Belarus, and professor at the department of differential equations and system analysis, faculty of mechanics and mathematics, Belarusian State University

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Published
2020-07-30
Keywords: error correcting codes, Bose – Chaudhuri – Hocquenghem codes, automorphisms of codes, norm decoding method, polynomial-norm decoding method
How to Cite
Kushnerov, A. V., & Lipnitski, V. A. (2020). Generic BCH codes. Polynomial-norm error decoding. Journal of the Belarusian State University. Mathematics and Informatics, 2, 36-48. https://doi.org/10.33581/2520-6508-2020-2-36-48
Issue
No 2 (2020): Journal of the Belarusian State University. Mathematics and Informatics
Section
Mathematical Logic, Algebra and Number Theory

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