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Mutually disjoint designs and new 5‐designs derived from groups and codes
Author(s) -
Araya Makoto,
Harada Masaaki,
Tonchev Vladimir D.,
Wassermann Alfred
Publication year - 2010
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20251
Subject(s) - combinatorics , mathematics , disjoint sets , combinatorial design , permutation (music) , simple (philosophy) , table (database) , discrete mathematics , computer science , physics , philosophy , epistemology , acoustics , data mining
The article gives constructions of disjoint 5‐designs obtained from permutation groups and extremal self‐dual codes. Several new simple 5‐designs are found with parameters that were left open in the table of 5‐designs given in (G. B. Khosrovshahi and R. Laue, t ‐Designs with t ⩾3, in “Handbook of Combinatorial Designs”, 2nd edn, C. J. Colbourn and J. H. Dinitz (Editors), Chapman & Hall/CRC, Boca Raton, FL, 2007, pp. 79–101), namely, 5−( v, k , λ) designs with ( v, k , λ)=(18, 8, 2 m ) ( m =6, 9), (19, 9, 7 m ) ( m =6, 9), (24, 9, 6 m ) ( m =3, 4, 5), (25, 9, 30), (25, 10, 24 m ) ( m =4, 5), (26, 10, 126), (30, 12, 440), (32, 6, 3 m ) ( m =2, 3, 4), (33, 7, 84), and (36, 12, 45 n ) for 2⩽ n ⩽17. These results imply that a simple 5−( v, k , λ) design with ( v, k )=(24, 9), (25, 9), (26, 10), (32, 6), or (33, 7) exists for all admissible values of λ. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 305–317, 2010