I have a problem in error-correcting codes.
Say we have a generator matrix of a linear binary code
$$g=\begin{pmatrix} 10011 \\ 01101 \end{pmatrix} $$
Q1: How many different codeword do we have? How many code bits can the code correct?
Say the generator matrix of a $(6,2)$ binary code is $$g=\begin{pmatrix} 101001\\ 011111 \end{pmatrix}$$
Q2: How many errors can it guarantee to detect?
My try:
For Q1:
The way I find the number of codeword is count the number of rows in $g$ and raise it as a power to 2. So the answer is $2^2=4$.
For detecting and correcting I’m not sure, should I find the hamming distance and subtract 1?
I hope someone can explain to me how I can find the number bits I can detect and correct.