Abstract
A nonstandard vector space is formulated, whose bases afford a representation of what is called a Hadamard matroid, M p . For prime p, existence of M p is equivalent to the existence of both a classical Hadamard matrix H( p, p) and a certain affine resolvable, balanced incomplete block design AR( p). An anomaly in the representable single element extension of a Hadamard matroid is discussed.
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