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Results tagged with finite-fields
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user 28104
A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.
2
votes
How to calculate log or exp of a value in GF(2^n) using log/exp table of GF((2^k)^m) where n...
Efficient algorithms to compute in finite fields are based on
Conway polynomials. Such algorithms are implemented in several
computer algebra systems, for example in GAP. For details, see e.g.
the cha …
- 19.6k
5
votes
Fixed space of the square of a symmetric matrix over $\mathbb{F}_2$
As Geoff Robinson has already said, the answer to the question is no.
In dimension $4$, there are in total $120$ counterexamples, of which
$96$ have kernel of dimension $1$, and $24$ have kernel of di …
- 19.6k
6
votes
The "interplay" between additive and multiplicative structure in a field
Large parts of number theory deal in some way with the interplay between addition and
multiplication in fields and subrings thereof. This concerns in particular all questions
which are related in so …
- 19.6k