I am trying to understand code distance, but I am not sure regarding the following scenario:
Assume that you have an information word M with m bits, that You code into a coding word using the following procedure:
- You take M and code it using a code you know nothing about. But you do know that its distance(code's distance) is k, and that k>2.
- You add to the word obtained in the last step a parity bit.
If you know that k is odd, does it necessarily mean that the distance of the code constructed by those two steps is necessarily k+1?
Well, I am not sure here. Code distance is basically the number of different bits, and the meaning of the second step in the procedure(adding a parity bit) is, according to my understanding, allowing the detection of any odd number of errors. Does it necessarily mean that the code constructed by those two steps is necessarily k+1?