code: def _encode_to_binary_string(message, on, off):
      
      def to_string(i, s):
          if i == 0 and s == off:
              return off * 4
          return s
      return ''.join(to_string(i, s) for i, s in enumerate(_encode_binary(message, on=on, off=off)))
docs: >>> message = "SOS"
      >>> _encode_to_binary_string(message, on='1', off='0')
      '101010001110111011100010101'
  
      >>> message = " SOS"
      >>> _encode_to_binary_string(message, on='1', off='0')
      '0000000101010001110111011100010101'