irreducible polynomial in a sentence

Examples

1. It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial.
2. An extension field is constructed from an underlying prime field ( the base field ) using an irreducible polynomial over the field.
3. In fact, this generator is a primitive element, and this polynomial is the irreducible polynomial that produces the easiest Euclidean division.
4. The fact that \ Phi _ n is an irreducible polynomial of degree \ varphi ( n ) in the Eisenstein's criterion.
5. Addition is simply XOR . Multiplication is modulo irreducible polynomial x ^ 8 + x ^ 4 + x ^ 3 + x + 1.
6. If, that is, one may choose as a quadratic non-residue, which allows us to have a very simple irreducible polynomial.
7. In the preceding theorem, one may replace " distinct irreducible polynomials " by " pairwise coprime polynomials that are coprime with their derivative ".
8. This means that it is generated by an element ? which is a root of an irreducible polynomial of degree " d ".
9. :: : Ok, now for n = 21, we first need an irreducible polynomial of degree 21 over GF ( 2 ).
10. The aim of factoring is usually to reduce something to  basic building blocks, such as numbers to prime numbers, or polynomials to irreducible polynomials.