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On a conjecture of jungnickel and tonchev for quasi-symmetric designs

โœ Scribed by Yury J. Ionin; Mohan S. Shrikhande

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
582 KB
Volume
2
Category
Article
ISSN
1063-8539

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โœฆ Synopsis

Jungnickel and Tonchev conjectured in [4] that if a quasi-symmetric design D is an s-fold quasi-multiple of a symmetric (v,k, A) design with (k, (sl)A) = 1, then D is a multiple. We prove this conjecture under any one of the conditions: s 5 7, k -1 is prime, or the design D is a 3-design. It is shown that for any fixed s, the conjecture is true with at most finitely many exceptions. The unique quasi-symmetric 3-(22,7,4) design is characterized as the only quasi-symmetric 3-design, which as a 2-design is an s-fold quasi-multiple with s = 1 (mod k).

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## Abstract It is wellโ€known that the number of designs with the parameters of a classical design having as blocks the hyperplanes in __PG__(__n, q__) or __AG__(__n, q__), __n__โ‰ฅ3, grows exponentially. This result was extended recently [D. Jungnickel, V. D. Tonchev, Des Codes Cryptogr, published on