Geodesic
Group ring ideals related to Reed--Muller codes
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 1, pp. 211-215.

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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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I. N. Tumaykin. Group ring ideals related to Reed--Muller codes. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 1, pp. 211-215. http://geodesic.mathdoc.fr/item/FPM_2016_21_1_a16/

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