Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs
Information Theory
2009-05-31 v2 Combinatorics
math.IT
Abstract
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect binary one-error-correcting code from its minimum distance graph is presented. Consequently, inequivalent such codes have nonisomorphic minimum distance graphs. Moreover, it is shown that the automorphism group of a minimum distance graph is isomorphic to that of the corresponding code.
Cite
@article{arxiv.0810.5633,
title = {Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs},
author = {Ivan Yu. Mogilnykh and Patric R. J. Östergård and Olli Pottonen and Faina I. Solov'eva},
journal= {arXiv preprint arXiv:0810.5633},
year = {2009}
}
Comments
4 pages. Accepted for publication in IEEE Transactions on Information Theory