We study systems of linear equations modulo two in $n$ variables
with three variables in each equation. We assume that the system has
a solution with $pn$ variables taking the value 1 for some value
$00$ it is hard to find a solution
of the same weight that satisfies at least a fraction
$c_p +\delta$ of the equations. The constant $c_p$ is
upper bounded by $.9$ for any value of $p$.