Recently, there are some measurement matrices that satisfy the restricted isometry principle, including the Gauss random matrix, Bernoulli random matrix, Hadamard matrix
, Toeplitz matrix, and random Fourier matrix [16-19].
So, the sequences that are derived by Walsh Hadamard matrix
play an important role in CDM-based communication technology.
On the other hand, for the Hadamard matrix
, which only has two distinct eigenvalues, the method always converges in two steps.
Magic state |H> is the +1-eigenstate of the Hadamard matrix
H = ([[sigma].sub.x] + [[sigma].sub.x])/ [square root of 2] that belongs to single qubit the Clifford group.
where [cross product] is the Hadamard matrix
product and matrix C of type p x p has elements
The entries [(-1).sup.u x v], for u, v [epsilon] [F.sup.m], form a Hadamard matrix
of order n = [2.sup.m].
In addition, the optimal PRVs can be selected by considering the rows of the Hadamard matrix
instead of the Sylvester-Hadamard sequences because of periodicity , .
Also, it is shown that if there exists a Hadamard matrix
of order 4d, then N((1,1; d), 8d - 2) = 4d and [bc.sub.2d]([K.sub.8d]) = 4d.
The design is focused on binary code, thus the biorthogonal Hadamard matrix
(denoted by [sub.b]H) is used as an example.
In this graph, the Hadamard matrix
is represented as a cylinder.