Looking at just this part of your code:

# this gives $result as 1, not 33.  Makes sense, 
# since $val == 4 evaluates to 1.  But, I want $result to 
# be assigned 33, based on the fact that $val == 4. 
$result = ($major_length == 4800) ? 18 
        : ($major_length ==  8552) 
            ? ($val == 4) : 33;
[download]

If I understand what you're asking for, you want:

    if ($major_length == 4800) {
        $result = 18;
    } elsif ($major_length == 8552) {
        if ($val == 4) {
            $result = 33;
        } else {
            # $result is Unspecified (see A below)
        }
    } else {
        # $result is Unspecified (see B below)
    }
[download]

You can do this with nested ternaries (though it's a little messy), but if you only want to use ternaries, you'll have to specify what to set $result to if none of the conditions is met (eg. $result = undef):

$result = ($major_length == 4800)? 18:
          (($major_length == 8552)?
           (($val == 4)? 33:
                        undef):        # see A above
                        undef);        # see B above
[download]

But it's messy as I said, and unless you really want to set $result to some value, it's probably better to use conditionals (eg. if...else), both for your clarity and the clarity of those who may read your code in the future ;-)