Equally spaced polynomial

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 _{{i=0}}^{{m}}x^{{si}}

for

i=0,1,\ldots ,m

or

ESP(x)=x^{{sm}}+x^{{s(m-1)}}+\cdots +x^{s}+1.

Properties

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

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

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