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% blocks.tex -- slide template
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% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\bgroup
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\begin{frame}[t]
\setlength{\abovedisplayskip}{5pt}
\setlength{\belowdisplayskip}{5pt}
\frametitle{Blocks}
\vspace{-20pt}
\begin{columns}[t,onlytextwidth]
\begin{column}{0.48\textwidth}
\begin{block}{Blocks}
$4\times k$ Matrizen mit $k=4,\dots,8$
\begin{center}
\begin{tikzpicture}[>=latex,thick]
\xdef\s{0.4}
\foreach \i in {0,...,31}{
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\end{tikzpicture}
\end{center}
\uncover<2->{%
Spalten sind $4$-dimensionale $\mathbb{F}_{2^8}$-Vektoren
}
\end{block}
\uncover<3->{%
\begin{block}{Zeilenshift}
\begin{center}
\begin{tikzpicture}[>=latex,thick]

\xdef\s{0.35}

\begin{scope}
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\end{scope}

\begin{scope}[xshift=3.5cm]
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	\node at \punkt{-1.5}{1.5} {$\rightarrow$};
\end{scope}

\end{tikzpicture}
\end{center}
\end{block}}
\end{column}
\begin{column}{0.50\textwidth}
\uncover<4->{%
\begin{block}{Spalten mischen}
Lineare Operation auf Spaltenvektoren mit Matrix
\begin{align*}
C&=\begin{pmatrix}
\texttt{02}_{16}&\texttt{03}_{16}&\texttt{01}_{16}&\texttt{01}_{16}\\
\texttt{01}_{16}&\texttt{02}_{16}&\texttt{03}_{16}&\texttt{01}_{16}\\
\texttt{01}_{16}&\texttt{01}_{16}&\texttt{02}_{16}&\texttt{03}_{16}\\
\texttt{03}_{16}&\texttt{01}_{16}&\texttt{01}_{16}&\texttt{02}_{16}
\end{pmatrix}
\\
\uncover<5->{
\det C
&=
\texttt{0a}_{16}
}
\uncover<6->{
\ne 0}
\uncover<7->{
\quad\Rightarrow\quad \exists C^{-1}
}
\end{align*}
\end{block}}
\uncover<8->{%
\begin{block}{Als Polynommultiplikation}
Spalten = Polynome in $\mathbb{F}_{2^8}[Z]/(Z^4-1)$,
\\
\uncover<9->{%
$C=\mathstrut$ Multiplikation mit
\[
c(Z) = \texttt{03}_{16}Z^3 + Z^2 + Z + \texttt{02}_{16}
\]
}
\end{block}}
\end{column}
\end{columns}
\end{frame}
\egroup