Neha Patil (Editor)

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:

E S P ( x ) = ∑ i = 0 m x s i for i = 0 , 1 , … , m

or

E S P ( x ) = x s m + x s ( m − 1 ) + ⋯ + x s + 1.

Properties

Over GF(2) the ESP has many interesting 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.

    References

    Equally spaced polynomial Wikipedia
    (Text) CC BY-SA