GF is small enough that you should construct an *antilog* table for it and save it for later reference rather than compute the polynomial form of or on the fly each time you need it. The
computer version of the *antilog* table is an array that stores the polynomial forms for in locations . For human use, the table
is constructed with two columns and looks something like this
The -th entry in the second column is the polynomial representation
of in abbreviated format. For example, is stated to be equal to which is shorthand for .
The entry for is obtained by shifting the entry
immediately above by one place to the left (inserting a on the
right) and if there is an term thus formed, removing it
and adding (i.e. XORing )
into the
rightmost bits. This process is easy to mechanize to produce
the antilog table by computer rather than by hand (which can be tedious
and mistake-prone).

**GF**15 S3 natural (

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**GF**(pn) and is also called the Galois field of order pn, in honor of the founder of finite field theory, Évariste Galois.

**GF**(p), where p is a prime number, is simply the ring of integers modulo p. That is, one can perform operations (addition, ...

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