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Longer titles found: Primitive polynomial (field theory) (view)

searching for Primitive polynomial 17 found (33 total)

Primitive part and content (1,725 words) [view diff] exact match in snippet view article find links to article

its content equals 1. Thus the primitive part of a polynomial is a primitive polynomial. Gauss's lemma for polynomials states that the product of primitive

Gauss's lemma (polynomials) (3,962 words) [view diff] exact match in snippet view article

that a primitive polynomial is irreducible over the integers if and only if it is irreducible over the rational numbers. More generally, a primitive polynomial

Factorization of polynomials (4,408 words) [view diff] exact match in snippet view article find links to article

is a primitive polynomial with integer coefficients. This defines a factorization of p into the product of an integer and a primitive polynomial. This

Finite field arithmetic (2,865 words) [view diff] exact match in snippet view article find links to article

where q = pt for some prime p and positive integer t, is called a primitive polynomial if all of its roots are primitive elements of GF(qn). In the polynomial

Irreducible polynomial (2,852 words) [view diff] exact match in snippet view article find links to article

is more accurately formulated by using the notion of primitive polynomial. A primitive polynomial is a polynomial over a unique factorization domain, such

Algebraic integer (1,497 words) [view diff] exact match in snippet view article find links to article

obtained by substituting xn in the polynomial for α. If P(x) is a primitive polynomial that has integer coefficients but is not monic, and P is irreducible

Rational root theorem (1,527 words) [view diff] exact match in snippet view article find links to article

the greatest common divisor of the coefficients so as to obtain a primitive polynomial in the sense of Gauss's lemma; this does not alter the set of rational

Data Matrix (3,015 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \alpha ^{8}+\alpha ^{5}+\alpha ^{3}+\alpha ^{2}+1=0} . The primitive polynomial is x 8 + x 5 + x 3 + x 2 + 1 {\displaystyle x^{8}+x^{5}+x^{3}+x^{2}+1}

QR code (9,926 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \alpha ^{8}+\alpha ^{4}+\alpha ^{3}+\alpha ^{2}+1=0} . The primitive polynomial is x 8 + x 4 + x 3 + x 2 + 1 {\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1}

Aztec Code (2,671 words) [view diff] exact match in snippet view article find links to article

Aztec code finite field polynomials Bits Field Primitive polynomial Generator polynomial (decimal coefficients) Used for 4 GF(16) x4+x+1 x5+11x4+4x3+6x2+2x+1

Eisenstein's criterion (3,592 words) [view diff] exact match in snippet view article find links to article

polynomials G, H (in case Q is not primitive, one applies the lemma to the primitive polynomial Q/c (where the integer c is the content of Q) to obtain a decomposition

Factorial (8,432 words) [view diff] exact match in snippet view article find links to article

nontrivial examples. The greatest common divisor of the values of a primitive polynomial of degree d {\displaystyle d} over the integers evenly divides d

Factorization (7,863 words) [view diff] exact match in snippet view article find links to article

factorization, the rational number is called the content, and the primitive polynomial is the primitive part. The computation of this factorization may

Cyclic code (5,187 words) [view diff] exact match in snippet view article find links to article

construction of cyclic codes generated by a product of a binomial and a primitive polynomial. The binomial has the form x c + 1 {\displaystyle x^{c}+1} for some

Reed–Solomon error correction (12,395 words) [view diff] exact match in snippet view article find links to article

Reed-Solomon algorithm % m is the number of bits per symbol % prim_poly: Primitive polynomial p(x). Ie for DM is 301 % k is the size of the message % n is the

Burst error-correcting code (9,235 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \ell =5} . Since p ( x ) {\displaystyle p(x)} is a primitive polynomial, its period is 2 5 − 1 = 31 {\displaystyle 2^{5}-1=31} . We confirm

Rectangular Micro QR Code (2,441 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \alpha ^{8}+\alpha ^{4}+\alpha ^{3}+\alpha ^{2}+1=0} . The primitive polynomial is x 8 + x 4 + x 3 + x 2 + 1 {\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1}