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Title: | Relative difference sets with n = 2 | Authors: | Arasu, K.T. Jungnickel, D. Siu Lun Ma Pott, A. |
Keywords: | Difference set Relative difference set |
Issue Date: | 16-Dec-1995 | Citation: | Arasu, K.T.,Jungnickel, D.,Siu Lun Ma,Pott, A. (1995-12-16). Relative difference sets with n = 2. Discrete Mathematics 147 (1-3) : 1-17. ScholarBank@NUS Repository. | Abstract: | We investigate the existence of relative (m, 2, k, λ)-difference sets in a group H × N relative to N. One can think of these as 'liftings' or 'extensions' of (m, k, 2λ)-difference sets. We have to distinguish between the difference sets and their complements. In particular, we prove: • - Difference sets with the parameters of the classical Singer difference sets describing PG(d, q) never admit liftings to relative difference sets with n = 2. • - Difference sets of McFarland and Spence type cannot be extended to relative difference sets with n = 2 (with possibly a few exceptions). • - Paley difference sets are not liftable. • - Twin prime power difference sets and their complements never lift. • - Menon-Hadamard difference sets cannot be extended to relative difference set with n = 2 if the order of the difference set is not a solution of a certain Pellian equation. Our results give strong evidence for the following conjecture: The only non-trivial difference sets which admit extensions to relative difference sets with n = 2 have the parameters of the complements of Singer difference sets with even dimension. © 1995. | Source Title: | Discrete Mathematics | URI: | http://scholarbank.nus.edu.sg/handle/10635/104043 | ISSN: | 0012365X |
Appears in Collections: | Staff Publications |
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