The generator polynomial of a t-error correcting is the LCM
of the minimal polynomials of the elements α, α2,
..., α2t.
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.
Consider the 2-error correcting BCH code of length 15
defined over GF(24) generated by the polynomial
x4+x+1.
Select the minimal polynomials
Observations
Consider the 3-error correcting BCH code of length 15
defined over GF(24) generated by the polynomial
x4+x+1.