#include <bitset>

template <typename T, int bits>
struct hamming_code {
  typedef std::bitset<(1 << bits)> value_type;

  static inline int block_length() {
    return (1 << bits) - 1;
  }

  static inline int message_length() {
    return (1 << bits) - bits - 1;
  }

  static inline bool parity(value_type b, int power)
  {
    T mask = 1 << power;
    int sum = 0;
    for (int bit_ix = 0; bit_ix < block_length(); bit_ix++) {
      if (!(bit_ix & mask)) continue;
      sum += b[ix];
    }
    return sum & 1;
  }

  static inline bool extended_parity(value_type b)
  {
    int sum = 0;
    for (int bit_ix = 0; bit_ix < block_length(); bit_ix++) {
      sum += b[ix];
    }
    return sum & 1;
  }

  static inline value_type encode(T t)
  {
    value_type ba(t);
  }
}