Equally spaced polynomial

Encyclopedia : E : EQ : EQU : Equally spaced polynomial

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An equally spaced polynomial (ESP) is a polynomial used in finite fields, specifically GF(2) (binary).

An s-ESP of degree sm can be written as:

[ESP(x) = \sum_^ x^] for [i = 0, 1, \ldots, m]

or

[ESP(x) = x^ + x^ + \cdots + x^s + 1]

Properties

Over GF(2) the ESP has many interest properties, including:

• The Hamming weight of the ESP is m + 1

A 1-ESP is known as an all one polynomial and has additional properties including the above.

 

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