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

Autor:	Mogilnykh, Ivan Yu., Östergård, Patric R. J., Pottonen, Olli, Solov'eva, Faina I.
Rok vydání:	2008
Předmět:	Computer Science - Information Theory Mathematics - Combinatorics
Zdroj:	IEEE Trans. Inform. Theory 55 (2009) 2622-2625
Druh dokumentu:	Working Paper
DOI:	10.1109/TIT.2009.2018338
Popis:	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. Comment: 4 pages. Accepted for publication in IEEE Transactions on Information Theory
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0810.5633 Zobrazit plný text záznamu View this record from Arxiv