I need to know what are the efficient algorithms to find all the irreducible polynomials of a given degree, say $d$ over a given finite field, say $\mathbb{F}_{p^n}.$

One way is to factorize the polynomial $x^{p^n}-x$, which is the product of all irreducible polynomials whose degree divides $n$, using factorization algorithms and collect all the degree $d$ factors. But I guess we are doing some extra job here. Are there better algorithms to find all irreducible polynomials of degree $d$ ?

I also want to know about the algorithms to find one irreducible polynomial of a given degree over a given finite field.

I need to know what are the efficient algorithms to find all the irreducible polynomials of a given degree, say $d$ over a given finite field, say $\mathbb{F}_{p^n}.$

One way is to factorize the polynomial $x^{p^{dn}}-x$, which is the product of all irreducible polynomials whose degree divides $d$, using factorization algorithms and collect all the degree $d$ factors. But I guess we are doing some extra job here. Are there better algorithms to find all irreducible polynomials of degree $d$ ?

I also want to know about the algorithms to find one irreducible polynomial of a given degree over a given finite field.

I need to know what are the efficient algorithms to find all the irreducible polynomials of a given degree, say $d$ over a given finite field, say $\mathbb{F}_{p^n}.$

One way is to factorize the polynomial $x^{p^n}-x$, which is the product of all irreducible polynomials whose degree divides $n$, using factorization algorithms and collect all the degree $d$ factors. But I guess we are some extra job here. Are there better algorithms to find all irreducible polynomials of degree $d$ ?

I also want to know about the algorithms to find one irreducible polynomial of a given degree over a given finite field.

I need to know what are the efficient algorithms to find all the irreducible polynomials of a given degree, say $d$ over a given finite field, say $\mathbb{F}_{p^n}.$

One way is to factorize the polynomial $x^{p^n}-x$, which is the product of all irreducible polynomials whose degree divides $n$, using factorization algorithms and collect all the degree $d$ factors. But I guess we are doing some extra job here. Are there better algorithms to find all irreducible polynomials of degree $d$ ?

I also want to know about the algorithms to find one irreducible polynomial of a given degree over a given finite field.