while (<DATA>) {
        s/\r?\n?//g; # remove newlines
        $a.=$_;
}
        # $a now contains the whole of DATA in one line
for (split(/;/,$a)) { # split into groups
        $b=0;
        for ( split (/,/) ) { # split into singles
                if (!$b++) { # first letter
                        # Store the first number of the
                        # group as a letter
                        $c = chr ( b($_) ); 
                } else {
                        # And scatter it wherever it needs
                        # to appear in the mystery string
                        @d[b($_)] = $c; 
                }
        }
}
print @d;
sub b { # convert from binary to decimal (littleendian)
        $a=$b=0;
        for(split(//,reverse$_[0])) {
                if($_) {
                        $a+=2**$b;
                }
                $b++;
        }
        return $a;
}

#"The unwritten geek credo states that originality and strangeness are
#good, and that blind conformity and stupidity are unforgivable."
#    http://samsara.circus.com/~omni/geek.html

__END__
0100000,0000100,0001100,0010001;1100001,0000101,0010011;1100011,001010
0;1100101,0001010,0001110,0010110;1101000,0001001,0010010;1101010,0000
000;1101011,0010101;1101100,0010000;1101110,0000110;1101111,0000111;11
10000,0001101;1110010,0001011,0001111,0010111;1110011,0000010;1110100,
0000011,0001000;1110101,0000001;
[download]

So, for instance, the first group of numbers is 32, 4, 12, 17. Thus a space (chr(32)) appears at positions 4, 12, and 17. I was a little disappointed that you didn't capitalize J or P, and that you didn't put a newline at the end. I'm always a little more impressed when little details like that are covered.