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Let (K, +, *) be an odd order presemifield with commutative multiplication. We show that the set of nonzero squares of (K, *) is a skew Hadamard difference set or a Paley type partial difference set in (K, +) according as q is congruent to 3 mod-ulo 4 or q is congruent to 1 modulo 4. Applying this result to the Coulter–Matthews presemifield and the… (More)

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