2007/10/31 by Lars Eirik Danielsen, Matthew G. Parker · 2 citations
Computer Science · Mathematics · #Coding theory and cryptography #Cooperative Communication and Network Coding #Error Correcting Code Techniques #cs.IT #math.CO #math.IT #msc:05C30 #msc:94B05
paper · pdf · doi:10.1007/s10623-008-9190-x
published as Des. Codes Cryptogr. 49(1-3), 161-170, 2008 · Presented at International Workshop on Coding and Cryptography (WCC 2007), 16-20 Apr. 2007, Versailles, France. (12 pages, 3 figures)
openalex publication_date 2008/03/05 · arxiv created 2009/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Orbits of graphs under the operation edge local complementation (ELC) are defined. We show that the ELC orbit of a bipartite graph corresponds to the equivalence class of a binary linear code. The information sets and the minimum distance of a code can be derived from the corresponding ELC orbit. By extending earlier results on local complementation (LC) orbits, we classify the ELC orbits of all graphs on up to 12 vertices. We also give a new method for classifying binary linear codes, with running time comparable to the best known algorithm.