Group Ring Ideals Related to Reed–Muller Codes
- Autores: Tumaykin I.1
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Afiliações:
- Lomonosov Moscow State University
- Edição: Volume 233, Nº 5 (2018)
- Páginas: 745-748
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241669
- DOI: https://doi.org/10.1007/s10958-018-3962-2
- ID: 241669
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Resumo
Reed–Muller codes are one of the most well-studied families of codes; however, there are till 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 ℳπ(m, k) over a prime field are powers of the radical RS 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 ℜSℳπ(m, k) that arise while studying the inclusions of the basic codes and radical powers.
Sobre autores
I. Tumaykin
Lomonosov Moscow State University
Autor responsável pela correspondência
Email: itumaykin@gmail.com
Rússia, Moscow