minimal degree in $R$ such that

(a) $\pi (\mathscr{C})=Rg(x)$, i.e. $g(x)$ is the generator polynomial of $\pi (\mathscr{C})$;

(b) $g(x)$ is a right divisor of $x^n-\alpha$;

(c) Every $c(x)\in\pi (\mathscr{C})$ can be written uniquely as $c(x)=f(x)g(x)\in R/R(x^n-\alpha)$, where $f(x)\in R$ has degree less than or equal to $n-\text{deg }g(x)$. Moreover, the dimension of $\mathscr{C}$ is equal to $n-\text{deg }g(x)$;

(d) If $g(x):=\sum\limits_{x=0}^k g_ix^i$, then $\mathscr{C}$ has a generator matrix $G$ given by $$\begin{aligned}
     G&=\begin{pmatrix} g(x)\\xg(x)\\ \vdots \\x^{n-k-1}g(x) \end{pmatrix}\\ &=
    \begin{pmatrix}
    g_0     &  g_1  &  \cdots  &  g_{k}  & 0          & 0         & \cdots  & 0  \\
    0         &  \theta(g_0)     &  \theta(g_1)     &  \cdots     & \theta(g_{k}) & 0         &  \cdots & 0  \\
    \vdots   &  \ddots &  \ddots  &  \ddots    & \ddots    & \ddots &  \ddots  & \vdots \\
    0         &  0        &   0         &  \theta^{n-k-1}(g_0)       &  \theta^{n-k-1}(g_1)      &   \cdots & \cdots  & \theta^{n-k-1}(g_{k}) \\
    \end{pmatrix}. \end{aligned}$$

For skew a-cyclic codes of $\mathbb{F}_q^n$ with $\theta (x):=x^{p^t}$, where $q=p^r$ for some prime $p$, $r\in\mathbb{Z}_{\geq 2}$ and an integer $t$ such that $1\leq t\leq r-1$, type the following Program $1$ before the Programs $2$ to $5$:

\[Prog-1\] 

    p:=...; r:=...; t:=...; F<w>:=GF(p^r); 
    R<X>:=TwistedPolynomials(F:q:=p^t);

The next Program $2$ constructs by the command +SD(n,a)+ all the 