The minimum number of minimal codewords in an \([n, k]\)-code and in graphic codes

DOI10.1016/j.dam.2014.11.015zbMath1311.05027OpenAlexW2058258197WikidataQ56926530 ScholiaQ56926530MaRDI QIDQ2341750

Patrick Solé, Carsten Thomassen, Seongmin Ok, R. E. L. Aldred, Adel N. Alahmadi, Romar B. dela Cruz

Publication date: 28 April 2015

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

Full work available at URL: https://doi.org/10.1016/j.dam.2014.11.015

zbMATH Keywords

matroid theorycycle code of graphsminimal codewords

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35) Combinatorial codes (94B25)

Related Items (5)

Counting Hamiltonian cycles in planar triangulations ⋮ On the minimum number of minimal codewords ⋮ Cycles in 5-connected triangulations ⋮ On the maximum number of minimal codewords ⋮ On the number of minimal codewords in codes generated by the adjacency matrix of a graph

Uses Software

• Magma
• nauty
• Traces

Cites Work

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• Lower bound of the Hadwiger number of graphs by their average degree
• The number of removable edges in 3-connected graphs
• The Magma algebra system. I: The user language
• On the number of cycles in 3-connected cubic graphs
• The extremal function for complete minors
• The maximum number of minimal codewords in long codes
• Practical graph isomorphism. II.
• An extremal function for contractions of graphs
• Graph decomposition with constraints on the connectivity and minimum degree
• Kuratowski's theorem
• Minimal vectors in linear codes
• On the Voronoi neighbor ratio for binary linear block codes
• A rank inequality for finite geometric lattices

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