multiplication of polynomials in $mathbb{F}_2[x]$
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Let $p(x) = 1 + x + x^2$ and $q(x) = 1 + x + x^3$. Then is the multiplication $p(x)q(x)$ obtained like this:
$$p(x)q(x)= (1 + x + x^2)(1 + x + x^3) = 1 +x +x^3 + x + x^2 + x^4 + x^2 + x^3 + x^5 $$
$$= 1 + x^4 + x^5?$$
proof-verification polynomials finite-fields irreducible-polynomials
edited Nov 21 at 11:27
Tianlalu
3,01021038
asked Nov 21 at 10:32
mandella
717521
add a comment |
up vote
0
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Let $p(x) = 1 + x + x^2$ and $q(x) = 1 + x + x^3$. Then is the multiplication $p(x)q(x)$ obtained like this:
$$p(x)q(x)= (1 + x + x^2)(1 + x + x^3) = 1 +x +x^3 + x + x^2 + x^4 + x^2 + x^3 + x^5 $$
$$= 1 + x^4 + x^5?$$
proof-verification polynomials finite-fields irreducible-polynomials
edited Nov 21 at 11:27
Tianlalu
3,01021038
asked Nov 21 at 10:32
mandella
717521
1
That is correct, but what has this to do withirreducible-polynomials?
– José Carlos Santos
Nov 21 at 10:33
1
Looks good to me.
– Arthur
Nov 21 at 10:33
@JoséCarlosSantos nothing, just that they are irreducible
– mandella
Nov 21 at 10:34
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $p(x) = 1 + x + x^2$ and $q(x) = 1 + x + x^3$. Then is the multiplication $p(x)q(x)$ obtained like this:
$$p(x)q(x)= (1 + x + x^2)(1 + x + x^3) = 1 +x +x^3 + x + x^2 + x^4 + x^2 + x^3 + x^5 $$
$$= 1 + x^4 + x^5?$$
proof-verification polynomials finite-fields irreducible-polynomials
edited Nov 21 at 11:27
Tianlalu
3,01021038
asked Nov 21 at 10:32
mandella
717521
Let $p(x) = 1 + x + x^2$ and $q(x) = 1 + x + x^3$. Then is the multiplication $p(x)q(x)$ obtained like this:
$$p(x)q(x)= (1 + x + x^2)(1 + x + x^3) = 1 +x +x^3 + x + x^2 + x^4 + x^2 + x^3 + x^5 $$
$$= 1 + x^4 + x^5?$$
proof-verification polynomials finite-fields irreducible-polynomials
proof-verification polynomials finite-fields irreducible-polynomials
edited Nov 21 at 11:27
Tianlalu
3,01021038
asked Nov 21 at 10:32
mandella
717521
edited Nov 21 at 11:27
Tianlalu
3,01021038
asked Nov 21 at 10:32
mandella
717521
edited Nov 21 at 11:27
Tianlalu
3,01021038
edited Nov 21 at 11:27
Tianlalu
3,01021038
edited Nov 21 at 11:27
Tianlalu
3,01021038
3,01021038
asked Nov 21 at 10:32
mandella
717521
asked Nov 21 at 10:32
mandella
717521
asked Nov 21 at 10:32
mandella
717521
717521
1
That is correct, but what has this to do withirreducible-polynomials?
– José Carlos Santos
Nov 21 at 10:33
1
Looks good to me.
– Arthur
Nov 21 at 10:33
@JoséCarlosSantos nothing, just that they are irreducible
– mandella
Nov 21 at 10:34
add a comment |
1
That is correct, but what has this to do withirreducible-polynomials?
– José Carlos Santos
Nov 21 at 10:33
1
Looks good to me.
– Arthur
Nov 21 at 10:33
@JoséCarlosSantos nothing, just that they are irreducible
– mandella
Nov 21 at 10:34
1
1
That is correct, but what has this to do with
irreducible-polynomials?– José Carlos Santos
Nov 21 at 10:33
That is correct, but what has this to do with
irreducible-polynomials?– José Carlos Santos
Nov 21 at 10:33
1
1
Looks good to me.
– Arthur
Nov 21 at 10:33
Looks good to me.
– Arthur
Nov 21 at 10:33
@JoséCarlosSantos nothing, just that they are irreducible
– mandella
Nov 21 at 10:34
@JoséCarlosSantos nothing, just that they are irreducible
– mandella
Nov 21 at 10:34
add a comment |
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1
That is correct, but what has this to do with
irreducible-polynomials?– José Carlos Santos
Nov 21 at 10:33
1
Looks good to me.
– Arthur
Nov 21 at 10:33
@JoséCarlosSantos nothing, just that they are irreducible
– mandella
Nov 21 at 10:34