Classification of Hadamard matrices of order 28

Abstract We constructed all inequivalent Hadamard matrices with Hall sets of order 28 and classified by K -matrices associated with Hadamard matrices except five matrices in our earlier work (Kimura, 1988)(see also Kimura, to appear; Kimura and Ohmori, 1987). In this paper we prove that Hadamard matrices with the trivial K -matrix are equivalent to the Paley matrix defined by the squares in GF(27). By this theorem we get a complete classification of Hadamard matrices of order 28 and we have inequivalent Hadamard matrices of order 28.