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Advances in Mathematics of Communications (AMC)
 

On quaternary complex Hadamard matrices of small orders
Pages: 309 - 315, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.309      Abstract        References        Full text (301.5K)           Related Articles

Ferenc Szöllősi - Department of Mathematics and its Applications, Central European University, H-1051, Nádor u. 9, Budapest, Hungary (email)

1 G. Auberson, A. Martin and G. Mennessier, On the reconstruction of a unitary matrix from its moduli, Commun. Math. Phys., 140 (1991), 417-436.       
2 S. Bouguezel, M. O. Ahmed and M. N. S. Swami, A new class of reciprocal-orthogonal parametric transforms, IEEE Trans. Circuits Syst. I, 56 (2009), 795-805.       
3 A. T. Butson, Generalized Hadamard matrices, Proc. Amer. Math. Soc., 13 (1962), 894-898.       
4 R. Craigen, Equivalence classes of inverse orthogonal and unit Hadamard matrices, Bull. Austral. Math. Soc., 44 (1991), 109-115.       
5 P. Diţă, Some results on the parametrization of complex Hadamard matrices, J. Phys. A, 20 (2004), 5355-5374.       
6 P. Diţă, Complex Hadamard matrices from Sylvester inverse orthogonal matrices, Open Sys. Inform. Dyn., 16 (2009), 387-405; see the errata at arXiv:0901.0982v2       
7 P. Diţă, Hadamard Matrices from mutually unbiased bases, J. Math. Phys., 51 (2010), 20.       
8 T. Durt, B.-H. Englert, I. Bengtsson and K. Życzkowski, On mutually unbiased bases, Intern. J. Quantum Inform., 8 (2010), 535-640.
9 U. Haagerup, Orthogonal maximal Abelian *-subalgebras of $n\times n$ matrices and cyclic $n$-roots, in "Operator Algebras and Quantum Field Theory (Rome),'' MA International Press, (1996), 296-322.       
10 M. Harada, C. Lam and V. D. Tonchev, Symmetric $(4,4)$-nets and generalized Hadamard matrices over groups of order $4$, Des. Codes Crypt., 34 (2005), 71-87.       
11 K. J. Horadam, "Hadamard Matrices and Their Applications,'' Princeton University Press, Princeton, 2007.       
12 M. N. Kolountzakis and M. Matolcsi, Complex Hadamard matrices and the spectral set conjecture, Collectanea Math., Extra (2006), 281-291.       
13 M. H. Lee and V. V. Vavrek, Jacket conference matrices and Paley transformation, in "Eleventh International Wokshop on Algebraic and Combinatorial Coding Theory,'' Pamporovo, Bulgaria, (2008), 181-185.
14 M. Matolcsi, J. Réffy and F. Szöllősi, Constructions of complex Hadamard matrices via tiling abelian groups, Open Sys. Inform. Dyn., 14 (2007), 247-263.       
15 T. S. Michael and W. D. Wallis, Skew-Hadamard matrices and the Smith normal form, Des. Codes Crypt., 13 (1998), 173-176.       
16 S. Popa, Orthogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory, 9 (1983), 253-268.       
17 F. Szöllősi, Parametrizing complex Hadamard matrices, European J. Combin., 29 (2008), 1219-1234.       
18 F. Szöllősi, Exotic complex Hadamard matrices and their equivalence, Crypt. Commun., 2 (2010), 187-198.       
19 W. Tadej and K. Życzkowski, A concise guide to complex Hadamard matrices, Open Syst. Inform. Dyn., 13 (2006), 133-177.       
20 T. Tao, Fuglede's conjecture is false in $5$ and higher dimensions, Math Res. Letters, 11 (2004), 251-258.       
21 R. F. Werner, All teleportation and dense coding schemes, J. Phys. A, 34 (2001), 7081-7094.       
22 G. Zauner, "Quantendesigns: Grundzäuge einer nichtkommutativen Designtheorie'' (in German), Ph.D thesis, Universität Wien, 1999; available online at http://www.mat.univie.ac.at/~neum/ms/zauner.pdf

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