On perfect and Reed-Muller codes over finite fields

DOI10.1134/S0032946021030017zbMath1495.94117OpenAlexW3203516005MaRDI QIDQ2068651

Alexander Mikhailovich Romanov

Publication date: 20 January 2022

Published in: Problems of Information Transmission (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0032946021030017

zbMATH Keywords

finite fieldHamming codeReed-Muller codeprojective Reed-Muller codeperfect codequasi-perfect codeMDS codeaffine Reed-Muller code

Mathematics Subject Classification ID

Linear codes (general theory) (94B05)

Related Items

On the number of \(q\)-ary quasi-perfect codes with covering radius 2, An enumeration of 1-perfect ternary codes, Constructions and invariants of optimal codes in the Lee metric

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The automorphism group of Generalized Reed-Muller codes
• The parameters of projective Reed-Müller codes
• On non-antipodal binary completely regular codes
• On non-full-rank perfect codes over finite fields
• A General Product Construction for Error Correcting Codes
• A Combinatorial Construction of Perfect Codes
• Fundamentals of Error-Correcting Codes
• Projective Reed-Muller codes
• Automorphism groups of homogeneous and projective Reed-Muller codes
• New generalizations of the Reed-Muller codes--I: Primitive codes
• On generalized ReedMuller codes and their relatives