Something else you could try is a file test before attempting to open the file:

if (-s $file) {
   open(FILE, $file) || die "open: $file - $!\n";
   # etc
} else {
   warn "There are currently no links :(\n"; # or similar msg
   exit();
}
[download]

Take a peek at this for a list of file test operators.

-- vek --