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-(ν,κ, λ) designs with (ν,κ, 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-(ν,κ, λ) design with (ν,κ)=(24,9), (25,9), (26,10), (32,6), or (33,7) exists for all admissible values of λ.
|Number of pages||13|
|Journal||Journal of Combinatorial Designs|
|Publication status||Published - 2010 Jul|
- Disjoint t-Design
- Extremal self-dual code
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics