Motivated by a problem posed by Hamming in 1980, we define even codes.They are Huffman type prefix codes with the additional property of beingable to detect the occurrence of an odd number of 1-bit errors in the message.We characterize optimal even codes and describe a simple method forconstructing the optimal codes. Further, we compare optimal even codeswith Huffman codes for equal frequencies. We show that the maximum encodingin an optimal even code is at most two bits larger than the maximum encodingin a Huffman tree. Moreover, it is always possible to choose an optimal evencode such that this difference drops to 1 bit. We compare averagesizes and show that the average size of an encoding in a optimal even treeis at least 1/3 and at most 1/2 of a bit larger thanthat of a Huffman tree. These values represent the overhead in the encodingsizes for having the ability to detect an odd number of errors in themessage. Finally, we discuss the case of arbitrary frequencies and describe some results for this situation.
