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- W1988974345 abstract "Generalizing a result of Ko and Ray-Chaudhuri ( Discrete Math. 39 (1982), 37–58), we show the following: Assume the existence of an affine difference set in G relative to N of even order n ≠2. If G is of the form G = N ⊕ H , where N is abelian, then n is actually a multiple of 4, say n = 4 k , and there exists a (4 k − 1, 2 k − 1, k − 1)-Hadamard difference set in N . More detailed considerations lead to variations of this result (under appropriate assumptions) which yield even stronger non-existence theorems. In particular, we show the non-existence of abelian affine difference sets of order n ≡ 4 mod 8 (with the exception n = 4) and of nilpotent affine difference sets of order n ≡ 2 mod 4 ( n ≠ 2). The latter result is the first general non-existence theorem in the non-abelian case." @default.
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- W1988974345 date "1989-11-01" @default.
- W1988974345 modified "2023-09-26" @default.
- W1988974345 title "Affine difference sets of even order" @default.
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- W1988974345 doi "https://doi.org/10.1016/0097-3165(89)90029-0" @default.
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