PD-sets for binary RM-codes and the codes related to the Klein quadric and to the Schubert variety of \(\mathrm{PG}(5,2)\)

DOI10.1016/j.disc.2006.11.057zbMath1169.94016OpenAlexW2146361334MaRDI QIDQ2468025

Hans-Joachim Kroll, Rita Vincenti

Publication date: 30 January 2008

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2006.11.057

zbMATH Keywords

linear codevarietyprojective systemPD-set

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Combinatorial structures in finite projective spaces (51E20)

Related Items

Partial permutation decoding for binary linear Hadamard codes, Partial permutation decoding for binary linear and \(\mathbb Z_4\)-linear Hadamard codes, Codes associated with the odd graphs, New advances in permutation decoding of first-order Reed-Muller codes, On linear codes admitting large automorphism groups, Reed-Muller codes and permutation decoding, On the existence of PD-sets: algorithms arising from automorphism groups of codes, Point-line incidence on Grassmannians and majority logic decoding of Grassmann codes, Linear codes from ruled sets in finite projective spaces

Cites Work

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• Permutation decoding for the binary codes from triangular graphs.
• PD-sets for the codes related to some classical varieties
• Minimum-weight codewords as generators of generalized Reed-Muller codes
• Minimal permutation sets for decoding the binary Golay codes (Corresp.)
• Geometric approach to higher weights