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The central problem in the present paper is the construction of symmetric and of skew-symmetric ( = skew) matrices C of order v, with diagonal elements 0 and other elements + 1 or — 1, satisfying The following necessary conditions are known: v ≡ 2 (mod 4) and a and b integers, for symmetric matrices C (Belevitch (1, 2), Raghavarao (14)), and v = 2 or v ≡ 0 (mod 4) for skew matrices C.
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Goethals et al. (1967) studied this question.
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