Hadamard codes matrix

Equations 39 show that with the Hadamard code, each unknown element x is observed N times with the same absolute weight factor namely, the absolute value of each of the matrix elements in the code... 

The specific values of information embedding rates appearing in these tables are due to the ECC used in these tests. The error correcting codewords we have used were the rows of the Hadamard matrices of varoius orders, together with their binary complementary sequences. The rate - R - of the code is determined from the order - h - of the Hadamard matrix by the relation R = where in our experiments h = 5,..., 12. 

Plankey et al have reported on the application of Hadamard transform spectrometry to the ultraviolet and visible spectral regions. The Hadamard technique utilizes the dispersed radiation from a conventional spectrometer. The radiation is passed through a coded mask, recombined, and recorded. The mask is composed of N slits, and N measurements are made with the mask in different positions. After measurement, N simultaneous equations must be solved with a Hadamard matrix to obtain the spectrum. The mask must be moved mechanically and reproducibly and a computer is used to solve the simultaneous equations. 

Examples of coding matrices include the Hadamard matrix and the Fourier matrix. The advantage of this method is the statistical improvement gained as a result of the increase in total scanning time. 

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