## Abstract A new lower bound on the number of nonβisomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2__n__ given in [12] by a factor of 8__n__βββ1 for every odd __n__β>β1, and for every even __n__ such that 4_
Bounds on the Number of Affine, Symmetric, and Hadamard Designs and Matrices
β Scribed by Clement Lam; Sigmund Lam; Vladimir D. Tonchev
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 118 KB
- Volume
- 92
- Category
- Article
- ISSN
- 0097-3165
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π SIMILAR VOLUMES
## Abstract It is wellβknown that the number of designs with the parameters of a classical design having as blocks the hyperplanes in __PG__(__n, q__) or __AG__(__n, q__), __n__β₯3, grows exponentially. This result was extended recently [D. Jungnickel, V. D. Tonchev, Des Codes Cryptogr, published on
This article replaces the incorrect version of the article first published in J Combin Designs 18 (2010), 450-461. The publisher apologizes for this error.
Let N = N (q) be the number of nonzero digits in the binary expansion of the odd integer q. A construction method is presented which produces, among other results, a block circulant complex Hadamard matrix of order 2 Ξ± q, where Ξ± β₯ 2N -1. This improves a recent result of Craigen regarding the asympt
## Abstract All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that