The syndrome polynomial table

1.        The polynomial x9 + 1 can be factorized as

X⁹ + 1 = (x + 1)(x² + x +1)( x⁶ + x³ +1)

The generator polynomial of a cyclic code with block length n = 9 is given as

g(x) = x⁶ + x³ + 1

(a) Determine the value of k.

(b) Find the parity check polynomial and generator polynomial of the dual cyclic code.

(c) Find the generator and parity check matrices of this cyclic code.

(d) Find the minimum distance of this code.

(e) Construct the syndrome polynomial table of this cyclic code.