Abstract
In this paper, we obtain several nonexistence results for abelian Hadamard difference sets. In particular, we prove that there are no Hadamard difference sets in abelian groups G = Z 2 × Z 2 × P, where | P| = p 2 α , α is odd and p is a prime congruent to 1 (mod 4). Also, we give a detailed proof for a connection between certain reversible Hadamard difference sets and projective three-weight codes which was claimed in Xiang and Chen (1996).
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