List questions from finite-fields

Published on 16 Apr 2016 - 13:07

27

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Basis of the special form

Published on 29 Mar 2026 - 16:28

154

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Geometric intuition for finite vector spaces?

Published on 16 Apr 2016 - 17:46

42

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Computing Multiplicative Character Values over Finite Fields

Published on 28 Mar 2026 - 11:25

145

Views

Elliptic curves with trivial Mordell–Weil group over certain fields.

Published on 27 Mar 2026 - 22:01

38

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$f(x) = x^2 + bx + a$ irreducible over $\Bbb F_p$ (finite field of $p$ prime elements) iff $(b^2 - 4a)^{\frac{p-1}{2}} = -1$ in $\Bbb F_p$

Published on 17 Apr 2016 - 16:35

28

Views

Order of a map $\Bbb F_{p^n}\to \Bbb F_{p^n}$which maps $x$ to $x^{p} -x$

Published on 01 Apr 2026 - 12:51

411

Views

Extension fields, and their cardinality and roots

Published on 20 Apr 2016 - 3:30

173

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Generating spanning sets for $\mathbb{F}^n_2$?

Published on 21 Apr 2016 - 21:07

159

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Subsequences of length $n$ always making a basis for $\mathbb{F}^n_2$?

Published on 21 Apr 2016 - 22:40

12.9k

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Confusion about elements in fields, like -1 in Z5

Published on 22 Apr 2016 - 18:39

186

Views

Expected length of spanning sequences of vectors

Published on 22 Apr 2016 - 23:53

206

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Finding exact isomorphism between finite fields given as quotient rings

Published on 24 Apr 2016 - 15:59

121

Views

Constructing an irreducible polynomial of degree $2$ over $\mathbb{F}_p$

Published on 25 Apr 2016 - 9:33

51

Views

In a binary code, all coordinates partake in at least one non-information set

Published on 31 Mar 2026 - 14:24

List Question

Product field of intermediate fields is field extension

Basis of the special form

Geometric intuition for finite vector spaces?

Computing Multiplicative Character Values over Finite Fields

Elliptic curves with trivial Mordell–Weil group over certain fields.

$f(x) = x^2 + bx + a$ irreducible over $\Bbb F_p$ (finite field of $p$ prime elements) iff $(b^2 - 4a)^{\frac{p-1}{2}} = -1$ in $\Bbb F_p$

Order of a map $\Bbb F_{p^n}\to \Bbb F_{p^n}$which maps $x$ to $x^{p} -x$

Extension fields, and their cardinality and roots

Generating spanning sets for $\mathbb{F}^n_2$?

Subsequences of length $n$ always making a basis for $\mathbb{F}^n_2$?

Confusion about elements in fields, like -1 in Z5

Expected length of spanning sequences of vectors

Finding exact isomorphism between finite fields given as quotient rings

Constructing an irreducible polynomial of degree $2$ over $\mathbb{F}_p$

In a binary code, all coordinates partake in at least one non-information set

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