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

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

References in corpus (1)

• The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification

Cited by in corpus (6)

• The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification
• The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
• Computational complexity of reconstruction and isomorphism testing for designs and line graphs
• On weak isometries of Preparata codes
• On the minimum distance graph of an extended Preparata code
• On the extention of propelinear structures of Nordstrom-Robinson code to Hamming code