all one polynomial

An all one polynomialMathworldPlanetmathPlanetmathPlanetmath (AOP) is a polynomial used in finite fieldsMathworldPlanetmath, specifically GF(2). The AOP is a 1-equally spaced polynomial.

An AOP of degree m can be written as follows:


Over GF(2) the AOP has many interesting properties, including:

Despite the fact that the Hamming weight is large, because of the ease of representation and other improvements there are efficient hardware and software implementations for use in areas such as coding theory and cryptography.

Title all one polynomial
Canonical name AllOnePolynomial
Date of creation 2013-03-22 15:00:26
Last modified on 2013-03-22 15:00:26
Owner Derk (34)
Last modified by Derk (34)
Numerical id 7
Author Derk (34)
Entry type Definition
Classification msc 12E10
Synonym all-one polynomial
Synonym AOP
Related topic CyclotomicPolynomial
Related topic ProofThatTheCyclotomicPolynomialIsIrreducible
Related topic FactoringAllOnePolynomialsUsingTheGroupingMethod