منابع مشابه
Certain Hadamard Designs
(2.1) F = C+C0 + C If A, B are two aggregates of elements of F we shall denote by AB the aggregate formed by adding each element of A to every element of B. We shall also denote the aggregate obtained by taking A a times by a A. Then we have the following Lemma 1. If p'=l (mod 4), then pl1 C0Ce = ——(C. + o, 4 , pl 1 p'-S pl-i (2.2) 0-, = ^-—— C + Í-—— C. + --C., 2 4 4 ¿i _ i ¿i _ i ¿i _ s c. = ...
متن کاملOn affine designs and Hadamard designs with line spreads
Rahilly [10] described a construction that relates any Hadamard design H on 4m−1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m, 4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m, 4) if, and only if, H is the classical design of points and hyperplanes in PG(2m...
متن کاملConstructing Hadamard matrices from orthogonal designs
The Hadamard conjecture is that Hadamard matrices exist for all orders 1,2, 4t where t 2 1 is an integer. We have obtained the following results which strongly support the conjecture: (i) Given any natural number q, there exists an Hadamard matrix of order 2 q for every s 2 [2log2 (q 3)]. (ii) Given any natural number q, there exists a regular symmetric Hadamard matrix with constant diagonal of...
متن کاملStructure and automorphism groups of Hadamard designs ∗
Let n be the order of a Hadamard design, and G any finite group. Then there exists many non-isomorphic Hadamard designs of order 212|G|+13n with automorphism group isomorphic to G.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.2307/2038298