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- W2070888906 abstract "Given any natural number q > 3 we show there exists an integer t ⩽ [2log2(q − 3)] such that an Hadamard matrix exists for every order 2sq where s > t. The Hadamard conjecture is that s = 2. This means that for each q there is a finite number of orders 2υq for which an Hadamard matrix is not known. This is the first time such a statement could be made for arbitrary q. In particular it is already known that an Hadamard matrix exists for each 2sq where if q = 2m − 1 then s ⩾ m, if q = 2m + 3 (a prime power) then s ⩾ m, if q = 2m + 1 (a prime power) then s ⩾ m + 1. It is also shown that all orthogonal designs of types (a, b, m − a − b) and (a, b), 0 ⩽ a + b ⩽ m, exist in orders m = 2t and 2t+2 · 3, t ⩾ 1 a positive integer." @default.
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- W2070888906 date "1976-09-01" @default.
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- W2070888906 title "On the existence of Hadamard matrices" @default.
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- W2070888906 doi "https://doi.org/10.1016/0097-3165(76)90062-5" @default.
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