In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length)...

coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over...

Reed–Solomon codes could use the BCH scheme of using a fixed generator polynomial, making such codes a special class of BCH codes, but Reed–Solomon codes based...

Specification of a CRC code requires definition of a so-called generator polynomial. This polynomial becomes the divisor in a polynomial long division, which...

polynomial g {\displaystyle g} . This must be a divisor of x n − 1 {\displaystyle x^{n}-1} . It follows that every cyclic code is a polynomial code....

In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight. Let C ⊂ F 2...

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition...

code seen in practice deviates confusingly from "pure" division, and the register may shift left or right. As an example of implementing polynomial division...

with initial root = 0 to obtain generator polynomials. The Reed–Solomon code uses one of 37 different polynomials over F 256 {\displaystyle \mathbb {F} _{256}}...

In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a...

In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms...

problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity...

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the...

Gustave Solomon in 1960, Reed–Solomon codes use univariate polynomials to form codewords, by evaluating polynomials of sufficiently small degree at the...

for this code is based on the evaluation of multilinear polynomials with m variables and total degree at most r. Every multilinear polynomial over the...

with initial root = 1 to obtain generator polynomials. The Reed–Solomon code uses different generator polynomials over F 256 {\displaystyle \mathbb {F} _{256}}...

In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through...

mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite field GF(pm). This means that a polynomial F(X) of degree m...

A binary code is called an even code if the Hamming weight of each of its codewords is even. An even code should have a generator polynomial that include...

In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number...

from an arbitrary field, its reciprocal polynomial or reflected polynomial, denoted by p∗ or pR, is the polynomial p ∗ ( x ) = a n + a n − 1 x + ⋯ + a 0...

the code. There are many types of linear block codes, such as Cyclic codes (e.g., Hamming codes) Repetition codes Parity codes Polynomial codes (e.g...

task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial function on the...

convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a...

Gray code or the natural binary code. The arrangement of taps for feedback in an LFSR can be expressed in finite field arithmetic as a polynomial mod 2...

correcting codes (such as BCH codes) are linear codes over GF(2) (codes defined from vector spaces over GF(2)), or polynomial codes (codes defined as...

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike...

versions Polynomial codes, of which BCH codes are an example Reed–Solomon codes Reed–Muller code Algebraic geometry code Binary Goppa code Low-density...

writing polynomial coefficients of G F ( 2 m ) {\displaystyle GF(2^{m})} elements on m {\displaystyle m} successive rows. Decoding of binary Goppa codes is...

Optimal Rectangular Code (ORC) is applied. This code is a combination of a parity track and polynomial code similar to a CRC, but structured for error correction...