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Bounds on the Number of Affine, Symmetric, and Hadamard Designs and Matrices

✍ 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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πŸ“œ SIMILAR VOLUMES


Bounds on the number of Hadamard designs
✍ Clement Lam; Sigmund Lam; Vladimir D. Tonchev πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 183 KB

## Abstract A new lower bound on the number of non‐isomorphic 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__β€‰βˆ’β€‰1 for every odd __n__ > 1, and for every even __n__ such that 4_

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## Abstract It is well‐known 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

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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

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## 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