Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs
arXiv:0810.5633 · doi:10.1109/TIT.2009.2018338
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.
4 pages. Accepted for publication in IEEE Transactions on Information Theory