Other monks have already provided excellent optimizations for this particular case. I'd like to add a more modest optimization which applies to your original code and is more generally useful:

Don't make unnecessary comparisons.

In the original implementation, you're making eight comparisons on each pair of characters when you only need two. 

if (${$strings[$i]}[$k]) {
  if (${$strings[$j]}[$k]) {
    $c11++;
  } else {
    $c10++;
  }
} else {
  if (${$strings[$j]}[$k]) {
    $c01++;
  } else {
    $c00++;
  }
}

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In reply to Re: Speeding permutation counting by dsheroh
in thread Speeding permutation counting by albert

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