This is a problem solving in MATLAB
(X8,X7,X6,X4 means 8th,7th,6th,4th power of X, a2 , a3, a4 means 2nd,3rd,4th power of a too )
A cyclic code is generated by g(X) = X8 + X7 + X6 + X4 + 1
a) Show that its length is 15
b) Find the generator matrix and parity check matrix in modified-echelon canonical form for this code.
c) Devise a linear switching circuit for encoding using k = 7 stages and one using n – k = 8 stages.
d) Show that a , a2 , a3 , and a4 are roots of g(X), where a; is a root of X4 + X + 1
i am attaching the document form of the problem so please make sure you look at it.