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3 exercise(s) shown, 0 hidden
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Work out the formula of the basic circulant almost Hadamard matrix
[[math]]
L_N=\frac{1}{\sqrt{N}}
\begin{pmatrix}
1&-\cos^{-1}\frac{\pi}{N}&\cos^{-1}\frac{2\pi}{N}&\ldots\ldots&\cos^{-1}\frac{(N-1)\pi}{N}\\
\cos^{-1}\frac{(N-1)\pi}{N}&1&-\cos^{-1}\frac{\pi}{N}&\ldots\ldots&-\cos^{-1}\frac{(N-2)\pi}{N}\\
\vdots&\vdots&\vdots&&\vdots\\
\vdots&\vdots&\vdots&&\vdots\\
-\cos^{-1}\frac{\pi}{N}&\cos^{-1}\frac{2\pi}{N}&-\cos^{-1}\frac{3\pi}{N}&\ldots\ldots&1
\end{pmatrix}
[[/math]]
at [math]N=3,5,7,9,11[/math], and compute its [math]1[/math]-norm.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Compute the almost Hadamard matrix associated to the Fano plane,
[[math]]
I_7=\begin{pmatrix}
x&x&y&y&y&x&y\\
y&x&x&y&y&y&x\\
x&y&x&x&y&y&y\\
y&x&y&x&x&y&y\\
y&y&x&y&x&x&y\\
y&y&y&x&y&x&x\\
x&y&y&y&x&y&x
\end{pmatrix}
[[/math]]
and its [math]1[/math]-norm. Then do the same with the Paley biplane.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Draw the projective planes over [math]\mathbb F_q[/math] with [math]q=p^k[/math] small, and compute the associated almost Hadamard matrices, and their [math]1[/math]-norm.