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 Fundam. Prikl. Mat., 2016, Volume 21, Issue 1, Pages 211–215 (Mi fpm1713)

Group ring ideals related to Reed–Muller codes

I. N. Tumaykin

Lomonosov Moscow State University

Abstract: Reed–Muller codes are one of the most well-studied families of codes; however, there are still open problems regarding their structure. Recently a new ring-theoretic approach has emerged that provides a rather intuitive construction of these codes. This approach is centered around the notion of basic Reed–Muller codes. It is known that basic Reed–Muller codes $\mathcal{M}_{\pi}(m,k)$ over a prime field are powers of the radical $\mathfrak{R}_S$ of a corresponding group algebra and over a nonprime field there are no such equalities, except for trivial ones. In this paper, we consider the ideals $\mathfrak{R}_S \mathcal{M}_{\pi}(m,k)$ that arise while studying the inclusions of the basic codes and radical powers.

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English version:
Journal of Mathematical Sciences (New York), 2018, 233:5, 745–748

UDC: 512.552.7+512.624.95

Citation: I. N. Tumaykin, “Group ring ideals related to Reed–Muller codes”, Fundam. Prikl. Mat., 21:1 (2016), 211–215; J. Math. Sci., 233:5 (2018), 745–748

Citation in format AMSBIB
\Bibitem{Tum16} \by I.~N.~Tumaykin \paper Group ring ideals related to Reed--Muller codes \jour Fundam. Prikl. Mat. \yr 2016 \vol 21 \issue 1 \pages 211--215 \mathnet{http://mi.mathnet.ru/fpm1713} \transl \jour J. Math. Sci. \yr 2018 \vol 233 \issue 5 \pages 745--748 \crossref{https://doi.org/10.1007/s10958-018-3962-2} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85050924153} 

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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. K. V. Vedenev, V. M. Deundyak, “The structure of finite group algebra of a semidirect product of abelian groups and its applications”, Chebyshevskii sb., 20:3 (2019), 107–123
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