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

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4 Author(s)
Mogilnykh, I.Yu. ; Sobolev Inst. of Math., Novosibirsk State Univ., Novosibirsk ; Ostergard, P.R.J. ; Pottonen, O. ; Solov'eva, F.I.

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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Information Theory, IEEE Transactions on  (Volume:55 ,  Issue: 6 )