Try:

my @counts = map { length } $string =~ /1(0*)/g;
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Basically, capture all the zeros, then map the length function on each, and return that.

Update: To get a count of characters after each 1, you could do something like

my @counts = map { length } $string =~ /1(?=(.*))/g;
[download]

We want to use the greediness of .*, so we do. We use look-ahead so that we can count the 1's that follow, but not eat them.

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