'00111',
          '01011',
          '01101',
          '01110',
          '10011',
          '10101',
          '10110',
          '11001',
          '11010',
          '11100'
[download]

So it looks like you're shifting the highest bit up by one, then the next highest bit, then the next, until you've run out of empty bits. How about something like (untested):

  use Bit::Vector;

  my $joins  = 2;
  my $splits = 3;
  my $length = $joins+$splits;
  my $start  = '0'x$joins . '1'x$splits;

  my $vector = Bit::Vector->new_Bin($length, $start);
  my @combinations = ();

  for my $pos ($joins-1..$length-1) { # 0-based, right?
    for my $bit ($splits-1..0) {
      $vector->bit_flip($pos+$bit);
      $vector->bit_flip($pos+$bit-1);
      push @combinations, $vector->to_Bin();
    }
  }
[download]

--
The hell with paco, vote for Erudil!
:wq