I have a matrix G of dimension 13x20. It is a full rank matrix. It is not in the standard form of a generator matrix. Now for the parity check matrix 'H', I need a standard representation H=[-P;I].
I used gauss Jordan elimination method, to convert 'G' into standard form, and the resulting matrix, is orthogonal with H matrix. But the H matrix, is not orthogonal to the G matrix.
So I did G*H1=[0]. and solved a system of linear equations to find the H1 that is orthogonal to the g matrix, I wass able to find only one vector, but for the remaining vecors, while solving the system of linear equations, the system is inconsistent(solution does not exist).
Because I was able to find a matrix from G that is orthogonal to H, why am I not able to find a H1 that is orthogonal to G?
Are there some mathematical methods available to do this??
regards, phani tej