Error-correcting codes from permutation groups

DOI10.1016/j.disc.2008.12.027zbMath1184.94273OpenAlexW2154926368MaRDI QIDQ1043942

Robert F. Bailey

Publication date: 10 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.disc.2008.12.027

zbMATH Keywords

permutation groupbasecovering designerror-correcting codegraph decomposition

Mathematics Subject Classification ID

Combinatorial codes (94B25) Combinatorial aspects of packing and covering (05B40) Subgroups of symmetric groups (20B35)

Related Items (14)

Permutation codes with specified packing radius ⋮ Error-correcting codes from \(k\)-resolving sets ⋮ Unnamed Item ⋮ Diagonally neighbour transitive codes and frequency permutation arrays ⋮ Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search ⋮ Decoding mixed errors and erasures in permutation codes ⋮ Permutation codes ⋮ Optimal permutation anticodes with the infinity norm via permanents of \((0,1)\)-matrices ⋮ Concatenated kernel codes ⋮ Unnamed Item ⋮ A construction and characterization of new sharply 3-transitive permutation sets contained in \(P\varGamma L(2,K)\) ⋮ Generalized covering designs and clique coverings ⋮ A new table of permutation codes ⋮ Backtracking Algorithms for Constructing the Hamiltonian Decomposition of a 4-regular Multigraph

Uses Software

• GAP

Cites Work

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• Uncoverings-by-bases for base-transitive permutation groups.
• Most primitive groups have messy invariants
• Fundamental algorithms for permutation groups
• Constructions for permutation codes in powerline communications
• Decoding the Mathieu group \(M_{12}\)
• Coding with permutations
• New constructions for covering designs
• Permutation codes for discrete channels (Corresp.)
• Powerline communication and the 36 officers problem
• Distance Enumerators for Permutation Groups
• Decoding generalised hyperoctahedral groups and asymptotic analysis of correctible error patterns

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