Tasks
Instructions
    Quick theory overview:
  • An \( [n,k] \) linear block code \( \mathcal{C} \) has dimension \( k \) and blocklength \( n \). The generator matrix of such a code is given by \( k \times n \) matrix. A systematic generator matrix has the structure \( [I_k | P] \) where \( I_k \) denotes a \( k \times k \) identity matrix and \( P \) is a \( k \times (n-k) \) matrix. A corresponding parity check matrix of the code \( \mathcal{C} \) can be obtained as the \( (n-k) \times n \) matrix denoted by \( [P^T | I_{n-k}] \).

    Procedure:
  • Enter the dimension of the given matrixes into the given boxes as row x column and click the Submit button.
    Next exercis fill out the entries of the sub-matrix \(P^T\) and click Submit.
  • Click Reset button to reset all your selected choices and restart.
  • Click the Next button and get exercise to fill out empty blocks with bits to find the structure of the sub-matrix \(P^T\). Click the Previous button to get an exercise on finding the dimensions of some given matrixes.

Consider a generator matrix \( G \) = \(\begin{bmatrix} 1 & 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 0 & 1 \end{bmatrix}\), find the dimensions of corresponding parity-check matrix \( H\), identity matrix \(I_{n-k}\), and sub-matrix \(P^T \).


Matrix Dimensions
Enter the dimensions of \( H \)
 
Enter the dimensions of \( I_{n-k} \)
 
Enter the dimensions of \( P^{T} \)
 
Observations