On the number of \(q\)-ary quasi-perfect codes with covering radius 2

DOI10.1007/s10623-022-01070-yzbMath1496.94087arXiv2111.00774OpenAlexW3208605955WikidataQ114849705 ScholiaQ114849705MaRDI QIDQ2161415

Alexander Mikhailovich Romanov

Publication date: 4 August 2022

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.00774

zbMATH Keywords

Galois geometryquasi-perfect codesgeneralized Reed-Muller codesswitching construction

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Combinatorial aspects of finite geometries (05B25) Combinatorial codes (94B25)

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An enumeration of 1-perfect ternary codes

Cites Work

• Ranks of \(q\)-ary 1-perfect codes
• On perfect and Reed-Muller codes over finite fields
• Minimum-weight codewords as generators of generalized Reed-Muller codes
• A General Product Construction for Error Correcting Codes
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• New generalizations of the Reed-Muller codes--I: Primitive codes
• Polynomial codes
• On generalized ReedMuller codes and their relatives
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