I'm trying to solve the following problem from the book Introduction to coding Theory:
I tried to solve it by myself but I think I was wrong: I tried to compute the parity check matrix and then to show that 6 columns of the parity check matrix are linearly dependent.. After that, I found a solution, but I'm having trouble understanding it.. That's the solution I found:
I cannot understand why is it useful to compute the rank of the matrix J+I and why since the rank is 4, then the dimension is 6. I had deduced te dimension directly from the definition of the parity check matrix: since G is 6x12, then the length of the code is 12 & the dimension is 6. Moreover: what can we deduce from the generator matrix? I can also not understand why then the minimum distance is either 3 or 6..
Thx in advance ;))