Convert this AoA:

my @control = (
  [  2, 13,  3, 16 ],
  [ 10,  1, 11,  6 ],
);
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To this...

#   0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 <-- Indicies rep
+resent original ints.
my @control = (
  [ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, ],
  [ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, ],
);
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So that you can take a test array, "@test = ( 1, 4, 7, 9 )" and ask if sum(@{control[$n]}[@test]) == 0

If you turn off warnings for undefined values in addition, you won't even need to worry about placing zeros; only place '1' where needed. ;)

That becomes an O(n) solution that benefits from the fact that array slices are fast, and List::Util::sum is XS. Wrap it in a grep, and it should fly:

my @valid_row_ix = grep { sum( @{$control[$_]}[@test] ) == 0 } 0 .. $#
+control;
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Update:

my @valid_row_ix = grep { List::MoreUtils::none { $_ == 1 } @{$control
+[$_]}[@test] } 0 .. $#control;
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...since it will short-circuit out of the "none" loop as soon as a 1 is detected, whereas 'sum' will look at all elements in your test array. However, the "$_==1" portion drops from XS back into a MULTICALL pure-Perl sub, which is more computationally expensive per iteration than a simple sum. Since the array you're testing seems to be small, my bet is with the 'sum' solution.