Find link

language:

Find link is a tool written by Edward Betts.

searching for Primitive element (finite field) 18 found (34 total)

alternate case: primitive element (finite field)

Glossary of field theory (2,063 words) [view diff] no match in snippet view article find links to article

is generated by S over F. Primitive element An element α of an extension field E over a field F is called a primitive element if E=F(α), the smallest extension

Primitive element theorem (1,911 words) [view diff] no match in snippet view article find links to article

In field theory, the primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element. This

Kummer theory (1,970 words) [view diff] no match in snippet view article find links to article

the Galois group, π is the Frobenius map minus the identity, and C the finite field of order p. Taking A to be a ring of truncated Witt vectors gives Witt's

Field extension (3,323 words) [view diff] no match in snippet view article find links to article

is called a simple extension and s {\displaystyle s} is called a primitive element of the extension. An extension field of the form K ( S ) {\displaystyle

List of abstract algebra topics (1,129 words) [view diff] no match in snippet view article find links to article

concepts Field (mathematics) Subfield (mathematics) Multiplicative group Primitive element (field theory) Field extension Algebraic extension Splitting field

Separable extension (3,075 words) [view diff] no match in snippet view article find links to article

characteristic zero is separable, and every algebraic extension of a finite field is separable. It follows that most extensions that are considered in

Splitting of prime ideals in Galois extensions (2,528 words) [view diff] no match in snippet view article find links to article

corresponds to the Frobenius automorphism in the Galois group of the finite field extension Fj / F. In the unramified case the order of DPj is f and IPj

Field (mathematics) (10,305 words) [view diff] no match in snippet view article

theory from 1928 through 1942, eliminating the dependency on the primitive element theorem. A commutative ring is a set that is equipped with an addition

Factorization of polynomials (4,370 words) [view diff] no match in snippet view article find links to article

fields, a fundamental step is a factorization of a polynomial over a finite field. Polynomial rings over the integers or over a field are unique factorization

BCH code (10,768 words) [view diff] no match in snippet view article find links to article

finite field (or Galois field) GF(q) with code length n = qm − 1 and distance at least d is constructed by the following method. Let α be a primitive

Cyclic code (5,214 words) [view diff] no match in snippet view article find links to article

correction. Let C {\displaystyle {\mathcal {C}}} be a linear code over a finite field (also called Galois field) G F ( q ) {\displaystyle GF(q)} of block length

Algebraic number field (8,499 words) [view diff] no match in snippet view article find links to article

{\displaystyle x\in K} . By the primitive element theorem, there exists such an x {\displaystyle x} , called a primitive element. If x {\displaystyle x} can

Separable algebra (1,777 words) [view diff] no match in snippet view article find links to article

only if L is separable as an associative K-algebra. If L/K has a primitive element a {\displaystyle a} with irreducible polynomial p ( x ) = ( x − a

Oval (projective plane) (4,186 words) [view diff] no match in snippet view article

only one: f(x) = x12 + x10 + η11x8 + x6 + η2x4 + η9x2, where η is a primitive element of GF(16) satisfying η4 = η + 1. In his 1975 paper Hall described

Disk encryption theory (3,772 words) [view diff] no match in snippet view article find links to article

I} is the number of the sector, α {\displaystyle \alpha } is the primitive element of GF ( 2 128 ) {\displaystyle {\text{GF}}(2^{128})} defined by polynomial

Data Matrix (3,098 words) [view diff] no match in snippet view article find links to article

256 {\displaystyle \alpha \in \mathbb {F} _{256}} is taken to be a primitive element satisfying α 8 + α 5 + α 3 + α 2 + 1 = 0 {\displaystyle \alpha ^{8}+\alpha

QR code (9,924 words) [view diff] no match in snippet view article find links to article

256 {\displaystyle \alpha \in \mathbb {F} _{256}} is taken to be a primitive element satisfying α 8 + α 4 + α 3 + α 2 + 1 = 0 {\displaystyle \alpha ^{8}+\alpha

Rectangular Micro QR Code (2,441 words) [view diff] no match in snippet view article find links to article

256 {\displaystyle \alpha \in \mathbb {F} _{256}} is taken to be a primitive element satisfying α 8 + α 4 + α 3 + α 2 + 1 = 0 {\displaystyle \alpha ^{8}+\alpha