Design a new double error correction code for HEX numbers, BCH(16,12), using GF(17). To save your calculation time, the 4x16 Vandermonde matrix is given here  (in array format). [ [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],   [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],   [1,4,9,16,8,2,15,13,13,15,2,8,16,9,4,1],   [1,8,10,13,6,12,3,2,15,14,5,11,4,7,9,16] ] Derive the generator matrix from the Vandermonde matrix. Briefly explain the working steps.

a) Manually (you do not need do any of this in code) create a graphical user interface such as the one depicted in Figure 1. Use the value provided in the CSV file on Canvas.   b) Minimum requirements are to always ask for 3 assignments – for this, you skip this step. For bonus credit, prompt the user to input the number of assignments to calculate statistics for.  In this case you would need to prompt the user via an input box for the total number of deliverables for which summary statistics will be calculated. You must verify that the user enters a value that can represent a valid integer number in the range [1, 6]. If the user enters a value that does not represent a number, the user enters a valid value but the value is outside of the allowed range, or the user enters a non-integer value, your program must display an error message box. Once the user acknowledges the error by pressing the “OK” button on the message box, your program must continue to display the input box asking for…

4) Construct the standard array for the (5 2) systematic code with generator matrix given by [1 0 10 1] G = lo 1 0 1 1] And find the minimum distance of the code, and discuss about error correcting capability of this code.

1] (Standard form): Let C be a binary (5; 3) code with generator matrix,G =  1 0 1 1 0         1 1 0 1 0        0 1 0 0 1(a) Reduce G to standard form.(b) Find a parity-check matrix for C.