Reconstructing extended perfect binary one-error-correcting codes from their minimum distance graphs

Mogilnykh, Ivan Yu., Ostergard, Patric R. J., Pottonen, Olli and Solov'eva, Faina I. (2009) Reconstructing extended perfect binary one-error-correcting codes from their minimum distance graphs. IEEE Transactions on Information Theory, 55 6: 2622-2625. doi:10.1109/TIT.2009.2018338


Author Mogilnykh, Ivan Yu.
Ostergard, Patric R. J.
Pottonen, Olli
Solov'eva, Faina I.
Title Reconstructing extended perfect binary one-error-correcting codes from their minimum distance graphs
Journal name IEEE Transactions on Information Theory   Check publisher's open access policy
ISSN 0018-9448
1557-9654
Publication date 2009-01-01
Sub-type Article (original research)
DOI 10.1109/TIT.2009.2018338
Open Access Status Not Open Access
Volume 55
Issue 6
Start page 2622
End page 2625
Total pages 4
Place of publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Language eng
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.
Keyword Extended perfect binary code
Minimum distance graph
Reconstructibility
Weak isometry
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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