If the following is the output you were looking for, then you forgot to close the If
and For
blocks. Also, there are some issues, with using \leftarrow
instead of the packages \gets
and some other minor issues with your way of using math mode:
\documentclass{scrartcl}
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{float}
\begin{document}
\begin{minipage}{.6\linewidth}
\begin{algorithm}[H]
\caption{Brute-Force algorithm}
\begin{algorithmic}[1]
\State \textbf{Input:} dimension $d \in \mathbf{N}$, error rate $\tau \in \left[0,\frac{1}{2}\right)$
\State \textbf{Output:} secret $\mathbf{s}$
\State $n$ = $4d $(\( \frac{1}{2} \) - \(\tau\))$^{-2}$ ,
\State $ (A,b) \gets Orc^n_{d,\tau} $
\For {$s' \in \mathbf{F}^n_2$}
\If{$wt(As'+b) \leq t$}
return s'
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm}
\end{minipage}
\end{document}

document
environment and giving it adocumentclass
does not result in that output (but rather a series of errors. Are you sure, these are all the packages you are using?