Equally spaced polynomial

Template:One source 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:

<math>ESP(x) = \sum_{i=0}^{m} x^{si}</math> for <math>i = 0, 1, \ldots, m</math>

or

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

Properties

Over GF(2) the ESP - which then can be referred to as all one polynomial (AOP) - has many interesting properties, including:

• The Hamming weight of the ESP is m + 1.

A 1-ESP is known as an all one polynomial (AOP) and has additional properties including the above.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

References

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