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Mutually disjoint designs and new 5-designs derived from groups and codes

✍ Scribed by Makoto Araya; Masaaki Harada; Vladimir D. Tonchev; Alfred Wassermann

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
126 KB
Volume
18
Category
Article
ISSN
1063-8539

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✦ Synopsis

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 tβ©Ύ3, in β€œHandbook of Combinatorial Designs”, 2nd edn, C. J. Colbourn and J. H. Dinitz (Editors), Chapman & Hall/CRC, Boca Raton, FL, 2007, pp. 79–101), namely, 5βˆ’(v, k, Ξ») designs with (v, k, Ξ»)=(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 2β©½nβ©½17. These results imply that a simple 5βˆ’(v, k, Ξ») design with (v, k)=(24, 9), (25, 9), (26, 10), (32, 6), or (33, 7) exists for all admissible values of Ξ». Β© 2010 Wiley Periodicals, Inc. J Combin Designs 18: 305–317, 2010

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