  We consider a "configuration model" for random XORSAT which is a random
system of $n$ equations over $m$ variables in $\mathbb F_2$. Each equation is
of the form $y_1 + y_2 + \cdots + y_k = b$ where $k \geq 3$ is fixed, $y_1,
y_2, \cdots$ are variables (not necessarily distinct) and $b \in \mathbb F_2$.
The equations are chosen independently and uniformly at random with
replacement. It is known \cite{Dubois02, Dietzfelbinger10, pittel2016} that
there exists $\rho_k$ such that $m / n = \rho_k$ is a sharp threshold for the
satisfiability of this system. In this note we show that for the configuration
model, the width of SAT-UNSAT transition window for random $k$-XORSAT is
$\Theta(n^{-1/2})$ and also derive the exact scaling function.
