A useful tool for constructing linear codes

DOI10.1016/j.jalgebra.2021.05.019zbMath1483.94073OpenAlexW3177452763MaRDI QIDQ2042936

Bernardo Gabriel Rodrigues, Wolfgang D. Knapp

Publication date: 22 July 2021

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2021.05.019

zbMATH Keywords

automorphism grouplinear codeweight distributionrepresentation theorypermutation groupdual modulemoduleHamming weightdual codeMathieu groupsConway groupspermutation modulesymmetric permutation groupMacWilliams' identities

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Linear codes (general theory) (94B05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Combinatorial aspects of finite geometries (05B25) Combinatorial codes (94B25) Symmetric groups (20B30) Computational methods for problems pertaining to group theory (20-08)

Related Items (1)

On the binary codes of length 552 which admit the simple group Co₃ as a transitive permutation group

Uses Software

• GAP
• Magma

Cites Work

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• Codes with prescribed permutation group
• The Magma algebra system. I: The user language
• The \(2\)-modular characters of Conway's third group \(Co_ 3\)
• Permutation decoding for the binary codes from triangular graphs.
• A projective two-weight code related to the simple group \(\mathrm{Co}_1\) of Conway
• \(M_{24}\)-orbits of octad triples
• A design and a code invariant under the simple group \(Co_ 3\)
• Vector stabilizers and subgroups of Leech lattice groups
• Binary codes of strongly regular graphs
• On the codes related to the Higman-Sims graph
• Some designs and codes invariant under the simple group Co\(_{2}\)
• The 2-modular characters of Conway's group Co₂
• The Minimal Degrees of Faithful Representations of the Sporadic Simple Groups and their Covering Groups
• On the binary codes of length 552 which admit the simple group Co₃ as a transitive permutation group

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