Finite Fields - Galois Fields

Finite Fields - Examples

• modulo fields

Finite Fields - Properties

Every field 𝐹 has 𝑞=𝑝^𝑛 elements, where 𝑝 is prime and 𝑛≥1. This statement holds since 𝐹 may be viewed as a vector space over its prime field. The dimension of this vector space is necessarily finite, say 𝑛, which implies the asserted statement.

A field with 𝑞=𝑝^𝑛 elements can be constructed as the splitting field of the polynomial:

• 𝑓(𝑥) = 𝑥^𝑞 - 𝑥

TODO: https://en.wikipedia.org/wiki/Field_(mathematics)