Equidistributed sequence: Difference between revisions

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An '''equally spaced polynomial''' (ESP) is a [[polynomial]] used in [[finite field]]s, specifically GF(2) ([[binary numeral system|binary]]).
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An s-ESP of degree ''sm'' can be written as:
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:<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 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==
{{unreferenced|date=July 2008}}
 
[[Category:Field theory]]
[[Category:Polynomials]]

Revision as of 21:07, 21 February 2014

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