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) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial).
In coding theory, a polynomialcode 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...
Specification of a CRC code requires definition of a so-called generator polynomial. This polynomial becomes the divisor in a polynomial long division, which...
codeword polynomial. Here, codeword polynomial is an element of a linear code whose code words are polynomials that are divisible by a polynomial of shorter...
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition...
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the...
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a...
specific to the QR standard. For example, the generator polynomial used for the Version 1 QR code (21×21), when 7 error correction bytes are used, is: g...
code seen in practice deviates confusingly from "pure" division, and the register may shift left or right. As an example of implementing polynomial division...
problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity...
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...
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...
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...
convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a...
In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes...
Gustave Solomon in 1960, Reed–Solomon codes use univariate polynomials to form codewords, by evaluating polynomials of sufficiently small degree at the...
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...
algorithm that solves the task and runs in polynomial time exists, meaning the task completion time varies as a polynomial function on the size of the input to...
on division in the ring of polynomials over the finite field GF(2) (the integers modulo 2), that is, the set of polynomials where each coefficient is either...
versions Polynomialcodes, of which BCH codes are an example Reed–Solomon codes Reed–Muller codes Algebraic geometry codes Binary Goppa codes Low-density...
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...
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