For what block sizes is this checksum valid?
05AB1E, 10 8 bytes
Input is a list of bits.
gÑ¨ʒιOÈP

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Commented:
gÑ          # push the divisors of the length of the input
  ¨         # remove the last one (the length itself)
   ʒ        # filter this list on:
    ι       #   push [a[0::b], a[1::b], ..., a[(b - 1)::b]] where a is the input b the divisor
            #   this groups the digits from each group at the same index together
     O      #   sum each list
      ÈP    #   are all sums even?