Is it possible to say that the members in C are already arranged according to the Parity Check method because C is the Kernel of H? And then what is left to do in the circuit is to characterize where the error is and correct it?
Thanks, Ido
The code C is the kernel of the matrix H. As the kernel is a set, there is no inherent order assigned to the elements in it.
The circuit needs to identify the position of the error (if at all there is an error), and then needs to correct it.