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2018-04-11 17:35:11 +02:00
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@ -40,7 +40,7 @@ In the following, we work with $q$-ary lattices, for some prime number $q$, defi
is a shift of $\Lambda_q^{\perp} (\mathbf{A})$.
\end{definition}
\begin{definition}[Gaussian distribution over a lattice] \index{Lattices!Gaussian distribution}
\begin{definition}[Gaussian distribution over a lattice] \index{Probability!Gaussian distribution}
For a lattice~$\Lambda$, a vector $\mathbf{c} \in \RR^n$ and a real~$\sigma>0$, define the distribution function
$\rho_{\sigma,\mathbf{c}}(\mathbf{x}) \triangleq \exp(-\pi\|\mathbf{x}- \mathbf{c} \|^2/\sigma^2)$.
The discrete Gaussian distribution of support~$\Lambda$, parameter~$\sigma$ and center $\mathbf{c}$ is defined as