A global code invariant under the Higman-Sims group

DOI10.1016/0021-8693(82)90073-4zbMath0492.20011OpenAlexW2019142182MaRDI QIDQ1167810

David B. Wales, Robert Calderbank

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90073-4

zbMATH Keywords

Higman-Sims groupdoubly transitive permutation groupmonomial representationcodes over finite fields

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Coding theorems (Shannon theory) (94A24) Multiply transitive finite groups (20B20)

Related Items (18)

Chevalley groups of type \(G_ 2\) as the group of a trilinear form ⋮ 2-Designs and Codes from Simple Groups L 3(q) and Higman-Sims Sporadic Simple Group HS ⋮ Linear codes and doubly transitive symmetric designs ⋮ Permutation groups and binary self-orthogonal codes ⋮ Binary codes of some strongly regular subgraphs of the McLaughlin graph ⋮ The Hoffman-Singleton graph and its automorphisms ⋮ Two sporadic geometries related to the Hoffman-Singleton graph ⋮ Some designs and codes invariant under the simple group Co\(_{2}\) ⋮ Some designs and codes invariant under the Tits group ⋮ Finite groups ⋮ On the codes related to the Higman-Sims graph ⋮ geometry ⋮ A self-orthogonal doubly even code invariant under \(M^c L:2\) ⋮ A design and a code invariant under the simple group \(Co_ 3\) ⋮ Minimal binary 2-neighbour-transitive codes ⋮ Association schemes on triples and a ternary algebra ⋮ Some sporadic geometries related to PG(3,2) ⋮ The Hermitian two-graph and its code

Cites Work

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• Strongly regular graphs
• Equiangular lines, the graph extension theorem, and transfer in triply transitive groups
• The factors of a design matrix
• Quadratic residue codes and symplectic groups
• On the simple group of D.G. Higman and C.C. Sims
• A simple group of order 44,352,000
• Finite permutation groups of rank 3
• On Moore Graphs with Diameters 2 and 3
• Regular 2-Graphs
• Generalized quadratic residue codes
• The Graph Extension Theorem

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