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)=
m | |
\sum | |
i=0 |
xsi
i=0,1,\ldots,m
or
ESP(x)=xsm+xs(m-1)+ … +xs+1.
Over GF(2) the ESP - which then can be referred to as all one polynomial (AOP) - has many interesting properties, including:
A 1-ESP is known as an all one polynomial (AOP) and has additional properties including the above.[1]