consider the following code. the legal codewords are those 16-bit sequences in which the number of 1-bits is divisible by 4. that is, a codeword is legal if it is 16-bit long, and among these bits there are 0, 4, 8, 12, or 16 1-bits. how much is the hamming distance of this code, and how many single bit errors can this code detect and correct?