Using MATLAB, perform the following steps:

Input: An $11$th$-$degree polynomial $($over GF$(2)),$ with coefficients of the $11$th$-$degree term and the constant term set to $1.$ Therefore, the total number of candidates is $2^10.$

Output: Primitive polynomials. Generate a sequence using the polynomial and LFSR $($Linear Feedback Shift Register$).$

$2.$ Calculate s$($t$)=1-2*$ x$($t$).$

$3.$ Compute the autocorrelation function R$($tau$).$ R$($tau$)=\backslash$Sigma $($t $=0$ to $(2^11-2))($s$($t$)*$ s$($t $+$ tau$)).$ Here, the index of t $+$ tau is calculated modulo $(2^11-1).$

$4.$ If R$($tau$)$ has a maximum value of $2^11-1$ at tau$=0$ and consists only of $1$s and $-1$s otherwise, then it's a primitive polynomial.

Compare the speed of this computation using FFT as well.