Some Results on \(r\)-Row-Regular Circulant Partial Hadamard Matrices of Order \((k \times 2k)\)
DOI:
https://doi.org/10.26713/cma.v13i1.1734Keywords:
Hadamard matrix, Circulant matrix, Partial Hadamard matrix, Orthogonal designAbstract
This paper provides some new results on \(r\)-row-regular circular partial Hadamard matrices of order \((k\times 2k)\), and also discusses the possible linear relationship between \(r\) and \(k\). Furthermore, a method of constructing such a matrix is given.
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R. Craigen, G. Faucher, R. Low and T. Wares, Circulant partial Hadamard matrices, Linear Algebra and its Applications 439(11) (2013), 3307 – 3317, DOI: 10.1016/j.laa.2013.09.004.
P. J. Davis, Circulant Matrices, 2nd edition, Vol. 338, 1994, 250 pp, AMS Chelsea Publishing, New York (1994), URL: https://bookstore.ams.org/chel-338.
R. Euler, L. H. Gallardo and O. Rahavandrainy, Eigenvalues of circulant matrices and a conjecture of Ryser, Kragujevac Journal of Mathematics 45(5) (2021), 751 – 759, URL: https://imi.pmf.kg.ac.rs/kjm/pdf/accepted-finished/01600fd373df27b2cb120d21fe74373b_2536_08012019_032857/kjm_45_5-7.pdf.
K. J. Horadam, Hadamard Matrices and Their Applications, Princeton University Press, Princeton, NJ (2007), DOI: 10.1515/9781400842902.
Y.-L. Lin, F. K. H. Phoa and M.-H. Kao, Circulant partial Hadamard matrices: Construction via general difference sets and its application to fMRI experiments, Statistica Sinica 27(4) (2017), 1715 – 1724, DOI: 10.5705/ss.202016.0254.
P. K. Manjhi and A. Kumar, On the construction of Hadamard matrices, International Journal of Pure and Applied Mathematics 120(1) (2018), 51 – 58.
P. K. Manjhi, On permutation group and Fourier matrices, International Journals for Engineering Application and Management 4(4) (2018), 197 – 200.
H. J. Ryser, Combinatorial Mathematics, The Carus Mathematical Monographs Vol. 14, AMS and The Mathematical Association of America, John Wiley and Sons Inc., New York, 154 pages (1963).
J. Saberry and M. Yamada, Hadamard Matrices: Constructions using Number Theory and Linear Algebra, John Wiley and Sons Inc., 352 pages (2020).
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