Edge Local Complementation and Equivalence of Binary Linear Codes
Combinatorics
2009-08-24 v4 Information Theory
math.IT
Abstract
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.
Keywords
Cite
@article{arxiv.0710.2243,
title = {Edge Local Complementation and Equivalence of Binary Linear Codes},
author = {Lars Eirik Danielsen and Matthew G. Parker},
journal= {arXiv preprint arXiv:0710.2243},
year = {2009}
}
Comments
Presented at International Workshop on Coding and Cryptography (WCC 2007), 16-20 Apr. 2007, Versailles, France. (12 pages, 3 figures)