几类n2阶BCCB哈达码矩阵的构造
On the Construction of Several Types of BCCB Complex Hadamard Matrices of Order n2
DOI: 10.12677/PM.2018.86088, PDF,    国家自然科学基金支持
作者: 徐登明：中国民航大学中欧航空工程师学院，天津；闫茜茜：中国民航大学理学院，天津
关键词: 循环矩阵；循环块构成的循环矩阵；哈达码矩阵；Circulant Matrices； Circulant Matrices with Circulant Blocks； Hadamard Matrices
摘要: 本文主要目的是构造BCCB复哈达码矩阵。首先，我们给出了n2阶BCCB复矩阵是哈达码矩阵的一个充要条件，然后利用这个条件构造了几类BCCB复哈达码矩阵。最后，作为例子给出了三类16阶BCCB复哈达码矩阵。
Abstract: In this note, we study how to construct BCCB complex Hadamard matrices. We first give a necessary and sufficient condition for a BCCB complex matrix of order n2 to be Hadamard, and then use the condition to construct various types of BCCB complex Hadamard matrices. As an example, three new types of BCCB complex Hadamard matrices of order 16 are provided.
文章引用：徐登明, 闫茜茜. 几类n2阶BCCB哈达码矩阵的构造[J]. 理论数学, 2018, 8(6): 656-661. https://doi.org/10.12677/PM.2018.86088

参考文献

[1] Caidman, L., Aharonov, Y. and Albert, D.Z. (1987) How to Ascertain the Values of σx, σy and σz of a Spin-1/2 Particle. Physical Review Letters, 58, 1385-1387.
[Google Scholar] [CrossRef] 
[2] Englert, B.G. and Aharonov, Y. (2001) The Mean King’s Problem: Prime Degrees of Freedom. Physics Letters A, 284, 1-5.
[Google Scholar] [CrossRef] 
[3] Bandyopadhyay, S., Boykin, P.O., Roychowdhury, V. and Vatan, F. (2002) A New Proof for the Existence of Mutually Unbiased Bases. Algorithmica, 34, 512-528.
[Google Scholar] [CrossRef] 
[4] Brierley, S. (2009) Mutually Unbiased Bases in Low Dimensions. PhD Thesis, University of York, York.
[5] Wootters, W.K. and Fields, B.D. (1989) Optimal State-Determination by Mutually Unbiased Meas-urements. Annals of Physics, 191, 363-381.
[Google Scholar] [CrossRef] 
[6] Liu, J.Y., Yang, M.H. and Feng, K.Q. (2017) Mutually Unbiased Maximally Entangled Bases in . Quantum Information Processing, 16, 159.
[Google Scholar] [CrossRef] 
[7] Tao, Y.H., Nan, H, Zhang, J. and Fei, S.M. (2015) Mutually Unbiased Maxi-mally Entangled Bases in . Quantum Information Processing, 14, 2291-2300.
[Google Scholar] [CrossRef] 
[8] Xu, D.M. (2017) Construction of Mutually Unbiased Maximally Entangled Bases through Permutations of Hadamard Matrices. Quantum Information Processing, 16, 65.
[Google Scholar] [CrossRef] 
[9] Tadej, W. and Zyczkowski, K. (2006) A Concise Guide to Complex Hadamard Matrices. Open Systems and Information Dynamics, 13, 133-177.
[Google Scholar] [CrossRef] 
[10] Combescure, M. (2009) Block-Circulant Matrices with Circulant Blocks, Weil Sums, and Mutually Un-Biased Bases. II. The Prime Power Case. Journal of Mathematical Physics, 50, Article ID: 032104.
[Google Scholar] [CrossRef] 
[11] Karlsson, B.R. (2016) BCCB Complex Hadamard Matrices of Order 9, and MUBs. Linear Algebra and Its Applications, 501, 309-324.
[Google Scholar] [CrossRef] 
[12] Davis, P.J. (1979) Circulant Matrices. John Wiley and Sons, New York.

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