Find the lowest-rate cyclic code

Question

Response to the following problem:

Let

g(X) = X⁸ + X⁶ + X⁴ + X² + 1

be a polynomial over the binary field.

a. Find the lowest-rate cyclic code with generator polynomial g(X). What is the rate of this code?

b. Find the minimum distance of the code found in (a).

c. What is the coding gain for the code found in (a)?