Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs

Details Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs

2008-10-31

arxiv.org/abs/0810.5633v2

IEEE Trans. Inform. Theory 55 (2009) 2622-2625

Computer Science

Information Theory

4 pages. Accepted for publication in IEEE Transactions on Information Theory

Scientific paper

10.1109/TIT.2009.2018338

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.

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