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Model. Anal. Inform. Sist., 2015, Volume 22, Number 4, Pages 464–482 (Mi mais453)  

This article is cited in 6 scientific papers (total in 6 papers)

Algorithms for majority decoding of group codes

V. M. Deundyaka, Yu. V. Kosolapovb

a FGNU NII "Specvuzavtomatika", 51 Gazetniy lane, Rostov-on-Don, 344002, Russia
b South Federal University, 105/42 Bolshaya Sadovaya Str., Rostov-on-Don, 344006, Russia

Abstract: We consider a problem of constructive description and justification of the algorithms necessary for a practical implementation of the majority decoder for group codes specified as left ideals of group algebras. In addition to the algorithms needed to implement a classical decoder of J. Massey, it is built a generalization of the classical decoder for codes with unequal protection of characters, which in some cases could be better than the classic one. For use as a classical decoder of J. Massey and its generalization to group codes it was developed an algorithm for constructing decoding trees that lie at the core of these algorithms for majority decoding. Because group codes are defined as left ideals of group algebras, the decoding algorithm for constructing decoding trees allows to build all decoding trees from one tree. On the basis of the generalized decoding algorithm it was developed an algorithm for decoding group codes induced on the subgroup. Application of the developed decoders was illustrated by an example of Reed-Muller-Berman codes and group codes induced by them on a non-Abelian group of affine transformations. In particular, for Reed–Muller–Berman code description and justification of the algorithm for constructing one decoding tree are provided. This three is used for constructing all decoding trees and then it is a built decoder for Reed–Muller–Berman codes and codes induced by them.

Keywords: majority decoder, group algebra, group codes, Reed–Muller–Berman Codes.

DOI: https://doi.org/10.18255/1818-1015-2015-4-464-482

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Bibliographic databases:

UDC: 517.9
Received: 29.04.2015

Citation: V. M. Deundyak, Yu. V. Kosolapov, “Algorithms for majority decoding of group codes”, Model. Anal. Inform. Sist., 22:4 (2015), 464–482

Citation in format AMSBIB
\Bibitem{DeuKos15}
\by V.~M.~Deundyak, Yu.~V.~Kosolapov
\paper Algorithms for majority decoding of group codes
\jour Model. Anal. Inform. Sist.
\yr 2015
\vol 22
\issue 4
\pages 464--482
\mathnet{http://mi.mathnet.ru/mais453}
\crossref{https://doi.org/10.18255/1818-1015-2015-4-464-482}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3418467}
\elib{http://elibrary.ru/item.asp?id=24273048}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Deundyak, Yu. V. Kosolapov, “Kriptosistema na indutsirovannykh gruppovykh kodakh”, Model. i analiz inform. sistem, 23:2 (2016), 137–152  mathnet  crossref  mathscinet  elib
    2. V. M. Deundyak, Yu. V. Kosolapov, E. A. Lelyuk, “Dekodirovanie tenzornogo proizvedeniya $\mathrm{MLD}$-kodov i prilozheniya k kodovym kriptosistemam”, Model. i analiz inform. sistem, 24:2 (2017), 239–252  mathnet  crossref  elib
    3. V. M. Deundyak, Yu. V. Kosolapov, “On the Berger–Loidreau cryptosystem on the tensor product of codes”, J. Comp. Eng. Math., 5:2 (2018), 16–33  mathnet  crossref  mathscinet  elib
    4. K. V. Vedenev, V. M. Deundyak, “Kody v diedralnoi gruppovoi algebre”, Model. i analiz inform. sistem, 25:2 (2018), 232–245  mathnet  crossref  elib
    5. Yu. V. Kosolapov, A. N. Shigaev, “Ob algoritme rasschepleniya nositelya dlya indutsirovannykh kodov”, Model. i analiz inform. sistem, 25:3 (2018), 276–290  mathnet  crossref  elib
    6. K. V. Vedenev, V. M. Deundyak, “Svyaz kodov i idempotentov v diedralnoi gruppovoi algebre”, Matem. zametki, 107:2 (2020), 178–194  mathnet  crossref
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