(19, 9, 4) Hadamard designs and their residual designs
نویسندگان
چکیده
منابع مشابه
Skew Hadamard designs and their codes
Skew Hadamard designs (4n−1, 2n−1, n−1) are associated to order 4n skew Hadamard matrices in the natural way. We study the codes spanned by their incidence matrices A and by I +A and show that they are self-dual after extension (resp. extension and augmentation) over fields of characteristic dividing n. Quadratic Residues codes are obtained in the case of the Paley matrix. Results on the p−rank...
متن کاملCertain 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 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: Journal of Combinatorial Theory, Series A
سال: 1974
ISSN: 0097-3165
DOI: 10.1016/0097-3165(74)90049-1