I think the previous replies have misunderstood your question. If I understand correctly, you want to take a pair of strings, put them on top of each other, and read *down* the columns:

string A: 0 1 0 1
string B: 1 1 0 1
          | | | |
          | | | +--> 11
          | | +----> 00
          | +------> 11
          +--------> 01
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.. i.e, not just look at all the pairs of characters in an individual string..

Splitting each string into an array seems wasteful, as arrays are much more memory-heavy than strings. You can use substr to index into any position in the string to get individual characters.

Also, instead of 4 different cases of logic involving 4 similarly-named variables $c00 through $c11, you can use a hash to really simplify the code:

my @data = qw[
  111011001010011110100010100001
  111010000010010110000010000001
  000101011100001000110101110000
  000101111101001001111101111110
  111011001010111110100010100001
  000100010100000000010001010000
];

use Data::Dumper;

for my $i (0 .. $#data) {
  for my $j ($i+1 .. $#data) {

    my %counts;

    $counts{ substr($data[$i],$_,1) . substr($data[$j],$_,1) }++
        for 0 .. length($data[$i]) - 1;

    print Dumper \%counts;

  }
}
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Another cute solution is to use chop to trim off characters at a time from both strings. It generates these character-pairs in reverse order, but since you only care about the final count, it's ok. Since it modifies the string, you have to do it on a copy.

for my $i (0 .. $#data) {
  for my $j ($i+1 .. $#data) {
    my %counts;
    my ($str1, $str2) = @data[$i,$j];

    $counts{ chop($str1) . chop($str2) }++
        while length($str1) and length($str2);
    print Dumper \%counts;
  }
}
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