Paper Info
Title
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.
Year
DOI
Venue
2009
10.1109/TIT.2009.2018338
IEEE Transactions on Information Theory
Keywords
DocType
Volume
extended perfect binary,minimum distance,weak isometry,reconstructibility,hamming distance,index terms— minimum distance graph,constructive proof,nonisomorphic minimum distance graph,extended perfect binary code,minimum distance graph,automorphism group,corresponding code,graph theory,hamming codes,information theory,binary codes,automation,error correction code,sociotechnical systems,codeword,mathematics
Journal
55
Issue
ISSN
Citations 
6
IEEE Trans. Inform. Theory 55 (2009) 2622-2625
2
PageRank 
References 
Authors
0.39
8
4
Name
Order
Citations
PageRank
Ivan Yu. Mogilnykh1368.74
Patric R. J. Östergård260970.61
Olli Pottonen3868.99
Faina I. Solov'eva45914.78