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|Title:||Abelian Difference Sets Without Self-conjugacy|
|Source:||Arasu, K.T.,Ma, S.L. (1998). Abelian Difference Sets Without Self-conjugacy. Designs, Codes, and Cryptography 15 (3) : 223-230. ScholarBank@NUS Repository.|
|Abstract:||We obtain some results that are useful to the study of abelian difference sets and relative difference sets in cases where the self-conjugacy assumption does not hold. As applications we investigate McFarland difference sets, which have parameters of the form v = q d+1 (q d + q d-1 + ⋯ + q + 2), k = q d (q d + q d-1 + ⋯ + q + 1), λ = q d (q d-1 + q d-2 + ⋯ + q + 1), where q is a prime power and d a positive integer. Using our results, we characterize those abelian groups that admit a McFarland difference set of order k - λ = 81. We show that the Sylow 3-subgroup of the underlying abelian group must be elementary abelian. Our results fill two missing entries in Kopilovich's table with answer "no".|
|Source Title:||Designs, Codes, and Cryptography|
|Appears in Collections:||Staff Publications|
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