Naslov
A New Series of Regular Hadamard Matrices

Autori
Crnković, Dean

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Thirtieth Australasian Conference on Combinatorial Mathematics and Combinatorial, Computing, The University of Queensland, 5-9 December 2005 / - Brisbane, 2005, 39-39

Skup
Thirtieth Australasian Conference on Combinatorial Mathematics and Combinatorial Computing

Mjesto i datum
Brisbane, Australija, 05.12.2005. - 09.12.2005

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
regular Hadamard matrix; symmetric design; Menon design

Sažetak
T. Xia, M. Xia and J. Seberry proved (see [2]) the following statement: When k=q_1, q_2, q_1q_2, q_1q_4, q_2q_3N, q_3q_4N, where q_1, q_2 and q_3 are prime powers, q_1=3 (mod 4), q_2=3 (mod 8), q_3=5 (mod 8), q_4=7 or 23, N=2^a3^bt^2, a, b=0 or 1, t \neq 0 is an arbitrary integer, there exist regular Hadamard matrices of order 4k^2. The existence of some regular Hadamard matrice of order 4p^2, when p is a prime, p=7 (mod 16), is established in [1]. According to [1] and [2], there are just two values of k<100 for which the existence of a regular Hadamard matrix of order 4k^2 is still in doubt, namely k=47 and k=79. We prove the following assertion: Let p and 2p-1 be prime powers and p=3 (mod 4). Then there exists a symmetric design with parameters (4p^2, 2p^2 - p, p^2 - p). Thus there exists a regular Hadamard matrix of order 4p^2. In particular, there exists a regular Hadamard matrix of order 4(79^2)=24964. REFERENCES: [1] K.~H. Leung, S.~L. Ma and B.~Schmidt, New Hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16, preprint. [2] T.~Xia, M.~Xia, and J.~Seberry, Regular Hadamard matrices, maximum excess and SBIBD, Australasian Journal of Combinatorics, Vol. 27 (2003) pp. 263--275.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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