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Enumerator polynomial information


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

Let be a binary linear code length . The weight distribution is the sequence of numbers

giving the number of codewords c in C having weight t as t ranges from 0 to n. The weight enumerator is the bivariate polynomial

and 24 Related for: Enumerator polynomial information

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Enumerator polynomial

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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...

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Enumerator

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Look up enumerator in Wiktionary, the free dictionary. Enumerator may refer to: Iterator (computer science) An enumerator in the context of iteratees...

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Polynomial sequence

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equal to the degree of the corresponding polynomial. Polynomial sequences are a topic of interest in enumerative combinatorics and algebraic combinatorics...

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Computably enumerable set

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repetition of values may be necessary in this case. Diophantine: There is a polynomial p with integer coefficients and variables x, a, b, c, d, e, f, g, h, i...

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Chromatic polynomial

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The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a...

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P versus NP problem

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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...

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Bell polynomials

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In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling...

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Rook polynomial

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In combinatorial mathematics, a rook polynomial is a generating polynomial of the number of ways to place non-attacking rooks on a board that looks like...

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Enumeration algorithm

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preprocessing phase is generally assumed to be polynomial in the input. Backtracking: The simplest way to enumerate all solutions is by systematically exploring...

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Tutte polynomial

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The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays...

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List of algebraic coding theory topics

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check Damm algorithm Dual code EXIT chart Error-correcting code Enumerator polynomial Fletcher's checksum Forward error correction Forward-backward algorithm...

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Reciprocal polynomial

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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...

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Zernike polynomials

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

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Orthogonal polynomials

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orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...

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Ehrhart polynomial

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

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Local regression

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regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its most...

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Symmetric polynomial

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symmetric polynomial is a polynomial P(X1, X2, ..., Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally...

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Elementary symmetric polynomial

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elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...

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Algebraic number

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An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example...

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Vertex enumeration problem

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known to be NP-hard, more precisely, there is no algorithm that runs in polynomial time in the combined input-output size, unless P=NP. A 1992 article by...

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Schur polynomial

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In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the...

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Narayana polynomials

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Narayana polynomials are a class of polynomials whose coefficients are the Narayana numbers. The Narayana numbers and Narayana polynomials are named after...

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Gottlieb polynomials

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In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials given by ℓ n ( x , λ ) = e − n λ ∑ k ( 1 − e λ ) k ( n k ) ( x k...

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Generating function

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functions precisely corresponds to the generating functions that enumerate quasi-polynomial sequences of the form f n = p 1 ( n ) ρ 1 n + ⋯ + p ℓ ( n ) ρ...

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