Generator Polynomial

Instructions

Quick theory overview:

The generator polynomial of a t-error correcting is the LCM of the minimal polynomials of the elements α, α², ..., α^2t.
Refer to the following table

Procedure:

Initially, all the polynomials are in grey background.
Clicking on polynomial changes its background color to from grey to green. All the polynomials with green background are the selected polynomials.
To deselect a polynomial, click on it again. Its background color changes back to grey.
Select all the minimal polynomials and click on Submit.
Observations section displays whether all the correct polynomials are selected or not.
If all the correct minimal polynomials have been selected, a field to enter the generator polynomial will be displayed.
Use only lower case x in the field. Expressions like x² can be entered in the field by typing x^2 on the keyboard.
1, +, x, x^2, x^3, ..., x^10 and their combinations need to be entered in the field in this task. Do not enter any other symbols.
Enter the polynomials in either increasing order of degree (from the lowest degree term to the highest) or decreasing order of degree (from the highest degree term to the lowest). For example, only 1+x^2+x^7+x^8 or x^8+x^7+x^2+1 is allowed. Any other permutation is not allowed. For example x^7+1+x^2+x^8 is not allowed.
Enter the encoding polynomial in the field and click on Submit.
The correctness of the entered answer is displayed in Observations.
Next - Displays the next example.
Previous - Displays the previous example.
Reset - Clears all selected polynomials, input fields, and empties the Observations section for the current example. Use this to start over or try a different selection.