Group structure on projective spaces and cyclic codes over finite fields

DOI10.1006/ffta.1999.0268zbMath0989.94031OpenAlexW2128233906MaRDI QIDQ1570224

Isabelle Lucien, Gilles Lachaud, Robert Rolland, Dany-Jack Mercier

Publication date: 6 January 2002

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/3da37822202be84022112e3a966377abf8a07189

zbMATH Keywords

cyclic codeserror correcting codesprojective Reed-Muller codes

Mathematics Subject Classification ID

Combinatorial structures in finite projective spaces (51E20) Cyclic codes (94B15)

Cites Work

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• The parameters of projective Reed-Müller codes
• Homogeneous polynomials vanishing on the projective space \(\mathbb{P}^m(\mathbb{F}_q)\)
• Projective Reed-Muller codes
• Estimates for Soto-Andrade sums.
• Cyclic subcodes of generalized Reed-Muller codes
• New generalizations of the Reed-Muller codes--I: Primitive codes
• On generalized ReedMuller codes and their relatives