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Codes in Bipartite Distance‐Regular Graphs
Author(s) -
Bannai Eiichi
Publication year - 1977
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-16.2.197
Subject(s) - mathematics , combinatorics , bipartite graph , discrete mathematics , complete bipartite graph , line graph , strongly regular graph , edge transitive graph , regular graph , voltage graph , equivalence (formal languages) , graph , graph power
For each bipartition of a bipartite distance‐regular graph Г, there naturally corresponds another distance‐regular graph Γ ¯ called a halved graph. It is shown that the existence of a perfect e ‐code in a halved graph Γ ¯ is equivalent to the existence of a uniformly packed 2 e ‐code in Г with certain specific parameters. Using this equivalence, we show the non‐existence of perfect codes for two classes of distance‐regular graphs Γ ¯ corresponding to Г = Q k and Г = 2. O k .