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. 
@article{FPM_2016_21_1_a16,
     author = {I. N. Tumaykin},
     title = {Group ring ideals related to {Reed--Muller} codes},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {211--215},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_1_a16/}
}
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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/