Maybe something along the lines of:

c:\@Work\Perl>perl -wMstrict -e
"my @strings = qw(DOG COT BAL MAN);
 ;;
 use constant FMT => '%6s';
 ;;
 printf FMT, $_ for '', @strings;
 print qq{\n};
 ;;
 for my $row (@strings) {
   printf FMT, $row;
   for my $col (@strings) {
     my $d = diff($row, $col);
     printf FMT, $d;
     }
   print qq{\n};
   }
 ;;
 sub diff { return scalar ($_[0] ^ $_[1]) =~ tr/\0//c; }
"
         DOG   COT   BAL   MAN
   DOG     0     2     3     3
   COT     2     0     3     3
   BAL     3     3     0     2
   MAN     3     3     2     0
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Update: In the
    sub diff { return scalar ($_[0] ^ $_[1]) =~ tr/\0//c; }
function definition, the scalar call is not needed, but does no harm. (Assignment to a scalar imposes scalar context.)