Geodesic
The structure of Reed--Muller codes over a~nonprime field
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 231-258

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It is well known that Reed–Muller codes over a prime field are radical powers of a corresponding group algebra. The case of a nonprime field is less studied in terms of equalities and inclusions between Reed–Muller codes and radical powers. In this paper, we prove that Reed–Muller codes in the case of a nonprime field of arbitrary characteristic are distinct from radical powers and provide necessary and sufficient conditions for inclusions between these codes and the powers of the radical. 
@article{FPM_2020_23_3_a12,
     author = {I. N. Tumaikin},
     title = {The structure of {Reed--Muller} codes over a~nonprime field},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {231--258},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a12/}
}
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I. N. Tumaikin. The structure of Reed--Muller codes over a~nonprime field. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 231-258. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a12/