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The Structure of Reed–Muller Codes Over a Nonprime Field

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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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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    I. N. Tumaykin

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  1. I. N. Tumaykin
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Correspondence to I. N. Tumaykin.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 3, pp. 231–258, 2020.

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Tumaykin, I.N. The Structure of Reed–Muller Codes Over a Nonprime Field. J Math Sci 269, 422–441 (2023). https://doi.org/10.1007/s10958-023-06290-8

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  • DOI: https://doi.org/10.1007/s10958-023-06290-8

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