Field:F8

This article is about a particular field, i.e., a field unique up to isomorphism. View a complete list of particular fields

Definition

This is the unique field (up to isomorphism) having eight elements. It is denoted $F_{8}$ or $GF(8)$. It can be defined as:

$\!F_{2}[x]/(x^{3}+x+1)$.

where $F_{2}$ is the field of two elements.

Related groups

Group functor	Value	GAP ID
additive group	elementary abelian group:E8	(8,5)
multiplicative group	cyclic group:Z7	(7,1)
general affine group of degree one	general affine group:GA(1,8)	(56,11)
projective special linear group of degree two	projective special linear group:PSL(3,2)	(168,42)

GAP implementation

The field can be defined using GAP's GF function:

GF(8)