Some algebraic questions about the Reed-Muller code

DOI10.1016/j.jalgebra.2024.01.044arXiv2209.00169MaRDI QIDQ6203799

Xiang-Dong Hou

Publication date: 8 April 2024

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.00169

zbMATH Keywords

finite fieldgeneral linear groupReed-Muller codemodular representationcomposition seriesaffine linear group

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Modular representations and characters (20C20) Polynomials over finite fields (11T06) Representations of finite groups of Lie type (20C33)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Improved partial permutation decoding for Reed-Muller codes
• Enumeration of AGL\((\frac{m}{3}, \mathbb F_{p^3})\)-invariant extended cyclic codes
• The automorphism group of Generalized Reed-Muller codes
• Reed-Muller codes and permutation decoding
• Polynomial representations of \(GL_n\)
• On the modular representations of the general linear and symmetric groups
• On self-dual affine-invariant codes
• Irreducible modular representations of GL\(_ 2\) of a local field
• Enumeration of certain affine invariant extended cyclic codes
• \(GL(m,2)\) acting on \(R(r,m)/R(r-1,m)\)
• Covering radius of the Reed-Muller code \(R(1,7)\) -- a simpler proof
• The covering radius of the (128,8) Reed-Muller code is 56 (Corresp.)
• The permutation group of affine-invariant extended cyclic codes
• The Covering Radius of the Reed–Muller Code RM(m – 4, m) in RM(m – 3, m)
• On the Number of Irreducible Modular Representations of a Finite Group
• Some results on cyclic codes which are invariant under the affine group and their applications
• On cyclic codes that are invariant under the general linear group
• Permutation Decoding of Systematic Codes