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Alternate descriptions of finite fields

Instead of having a single polynomial-quotient (aka “rupture”) step $\mathbb{F}_p[X]/(P)$ with $P \in \mathbb{F}_p[X]$ irreducible, you can also construct finite fields in several steps, i.e., ...
Gro-Tsen's user avatar
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Alternate descriptions of finite fields

The field of $p^n$ elements is the splitting field of $x^{p^n}-x$ over the field of $p$ elements.
Gerry Myerson's user avatar
1 vote

Alternate descriptions of finite fields

Another way of representing finite fields that is sometimes used on computational algebra is via Zech logarithms: basically you represent all non-zero elements as powers of a fixed primitive root $\...
Max Horn's user avatar
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Alternate descriptions of finite fields

An alternate description that works for every finite field is the matrix representation: any finite field of order $q^m$ can be represented by a matrix algebra $\mathbb F_q[M]$ where $M$ is a $m\times ...
Reyx_0's user avatar
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