Mutually disjoint designs and new 5‐designs derived from groups and codes
Document Type
Article
Publication Date
5-2010
Abstract
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, 2m) (m=6, 9), (19, 9, 7m) (m=6, 9), (24, 9, 6m) (m=3, 4, 5), (25, 9, 30), (25, 10, 24m) (m=4, 5), (26, 10, 126), (30, 12, 440), (32, 6, 3m) (m=2, 3, 4), (33, 7, 84), and (36, 12, 45n) 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.
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Araya, M.,
Harada, M.,
Tonchev, V.,
&
Wassermann, A.
(2010).
Mutually disjoint designs and new 5‐designs derived from groups and codes.
Journal of Combinatorial Designs,
18(4), 305-317.
http://doi.org/10.1002/jcd.20251
Retrieved from: https://digitalcommons.mtu.edu/math-fp/101
Publisher's Statement
© 2010 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.20251