What is the minimum distance of the code

Question

Response to the following problem:

The polynomial X¹⁵ + 1 when factored yields

X¹⁵+1 = (X⁴+X³+1)(X⁴+X³+X²+X+1)(X⁴+X+1)(X²+X+1)(X+1)

a. Construct a systematic (15, 5) code using the generator polynomial

g(X) = (X⁴+X³+X²+X+1)(X⁴+X+1)(X²+X+1)

b. What is the minimum distance of the code?

c. How many random errors per codeword can be corrected?

d. How many errors can be detected by this code?

e. List the code words of a (15, 2) code constructed from the generator polynomial

g(X) = X¹⁵+1/X²+X+1

and determine the minimum distance.