Solve the following problem:
A (k + 1, k) block code is generated by adding 1 extra bit to each information sequence of length k such that the overall parity of the code (i.e., the number of 1s in each codeword) is an odd number. Two students, A and B, make the following arguments on error detection capability of this code.
1. Student A: Since the the weight of each codeword is odd, any single error changes the weight to an even number. Hence, this code is capable of detecting any single error.
2. Student B: The all-zero information sequence
ill be encoded by adding one extra 1 to generate the codeword
This means that there is at least one codeword of weight 1 in this code. Therefore, dmin = 1, and since any code can detect at most dmin - 1 errors, and for this code dmin - 1 = 0, this code cannot detect any errors. Which argument do you agree with and why? Give your explanation in one short paragraph.