Permutation groups and binary self-orthogonal codes

DOI10.1016/J.JALGEBRA.2006.06.001zbMath1172.94012OpenAlexW1985911268MaRDI QIDQ875108

Naoki Chigira, Masaaki Kitazume, Masaaki Harada

Publication date: 11 April 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.06.001

zbMATH Keywords

permutation groupsporadic simple groupself-orthogonal code and self-dual code

Mathematics Subject Classification ID

Combinatorial codes (94B25) General theory for finite permutation groups (20B05)

Related Items (6)

Extremal self-dual codes of length 64 through neighbors and covering radii ⋮ Self-dual codes related to the Rudvalis group ⋮ Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of \(M_{11}\) ⋮ On some codes from rank 3 primitive actions of the simple Chevalley group \(G_2(q) \) ⋮ On the classification of binary self-dual codes admitting imprimitive rank 3 permutation groups ⋮ On the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups

Uses Software

• Magma

Cites Work

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• A characterization of designs related to the Witt system S(5,8,24)
• A global code invariant under the Higman-Sims group
• The affine primitive permutation groups of degree less than 1000.
• A self-orthogonal doubly even code invariant under \(M^c L:2\)
• A design and a code invariant under the simple group \(Co_ 3\)
• Some self-dual codes invariant under the Hall-Janko group
• On the simple group of D.G. Higman and C.C. Sims
• Good self dual codes exist
• The primitive permutation groups of degree less than 2500.
• Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs

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