Group Ring Ideals Related to Reed–Muller Codes
- 作者: Tumaykin I.1
-
隶属关系:
- Lomonosov Moscow State University
- 期: 卷 233, 编号 5 (2018)
- 页面: 745-748
- 栏目: 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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详细
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.
作者简介
I. Tumaykin
Lomonosov Moscow State University
编辑信件的主要联系方式.
Email: itumaykin@gmail.com
俄罗斯联邦, Moscow