I might have accidentally broken my previous post, so I just post the final results here. Not because my solutions are faster (tux_a_fp is sloooooow), but as they show TIMTOWTDI

use Algorithm::FastPermute;

sub tux_a_fp {
    my ($length, $ones) = @_;
    my @l = ((0) x ($length - $ones), (1) x $ones);
    my %seen;
    permute { $seen{join "" => @l}++ } @l;
    [ keys %seen ];
    }

sub tux_for {
    my ($length, $ones) = @_;
    my $s1 = "1" x $ones;
    my $s0 = "0" x ($length - $ones);
    [   map  { substr unpack ("b*", $_), 0, $length }
        grep { $ones == unpack "%32b*" => $_ }
        map  { pack "L<", $_ }
        oct "0b$s1" .. oct "0b$s1$s0"
        ];
    }

sub tux_tr {
    my ($length, $ones) = @_;
    my $s1 = "1" x $ones;
    my $s0 = "0" x ($length - $ones);
    [   grep { $ones == tr/1/1/ }
        map  { substr unpack ("b*", pack "L<",$_), 0, $length }
        oct "0b$s1" .. oct "0b$s1$s0"
        ];
    }
[download]

update: another variation on recursion:

sub tux_recur {
    my ($length, $ones) = @_;
    $length          or  return [];
    $ones            or  return [ "0" x $length ];
    $ones == $length and return [ "1" x $length ];
    [ ( map { "0$_" } @{tux_recur ($length - 1, $ones    )} ),
      ( map { "1$_" } @{tux_recur ($length - 1, $ones - 1)} ),
      ];
    }
[download]

On my box ends between Eily and tybalt89. GrandFather is still the fastest:

Discipulus  0.103/s
tux_a_fp     1.43/s
choroba      1496/s
tybalt89_re  1558/s
tux_tr       1777/s
tux_for      2807/s
johngg       2828/s
Eily         2851/s
tux_recur    2889/s
tybalt89     3654/s
salva        4187/s
Eily_LanX    5110/s
GrandFather  6119/s
[download]