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|Title:||Difference Sets Corresponding to a Class of Symmetric Designs|
|Authors:||Ma, S.L. |
McFarland's difference set
|Source:||Ma, S.L.,Schmidt, B. (1997). Difference Sets Corresponding to a Class of Symmetric Designs. Designs, Codes, and Cryptography 10 (2) : 223-236. ScholarBank@NUS Repository.|
|Abstract:||We study difference sets with parameters (v, k, λ) = (ps(r2m - 1)/(r - 1), ps-1r2m-1, ps-2(r - 1)r2m-2), where r = (ps - 1)/(p -1) and p is a prime. Examples for such difference sets are known from a construction of McFarland which works for m = 1 and all p, s. We will prove a structural theorem on difference sets with the above parameters; it will include the result, that under the self-conjugacy assumption McFarland's construction yields all difference sets in the underlying groups. We also show that no abelian (160, 54, 18)-difference set exists. Finally, we give a new nonexistence prove of (189, 48, 12)-difference sets in ℤ3 × ℤ9 × ℤ7.|
|Source Title:||Designs, Codes, and Cryptography|
|Appears in Collections:||Staff Publications|
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