Abstract
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.
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