Edge Local Complementation and Equivalence of Binary Linear Codes

Details Edge Local Complementation and Equivalence of Binary Linear Codes Edge Local Complementation and Equivalence of Binary Linear Codes

2007-10-11

arxiv.org/abs/0710.2243v4

Des. Codes Cryptogr. 49(1-3), 161-170, 2008

Mathematics

Combinatorics

Presented at International Workshop on Coding and Cryptography (WCC 2007), 16-20 Apr. 2007, Versailles, France. (12 pages, 3 f

Scientific paper

10.1007/s10623-008-9190-x

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.

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