Question

Galois group of finite field extension

score 103 · Answer 1 · 2026-03-25 15:51:53

103

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Galois group of finite field extension

Published on 25 Mar 2026 - 15:51

score 176 · Answer 2 · 2018-11-12 09:54:50

176

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Nullity of the same matrix over a finite and infinite field

Published on 12 Nov 2018 - 9:54

score 53 · Answer 3 · 2018-11-14 19:28:46

53

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Definition of the d-th power residue symbol

Published on 14 Nov 2018 - 19:28

score 87 · Answer 4 · 2026-03-25 06:08:51

87

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$N$ random points make a random polynomial?

Published on 25 Mar 2026 - 6:08

score 851 · Answer 5 · 2026-03-25 22:26:07

851

Views

Multiplicative inverse of a polynomial in $GF(8)$

Published on 25 Mar 2026 - 22:26

score 26 · Answer 6 · 2026-03-26 01:25:13

26

Views

Finding the number of roots of u(X,Y) under certain restrictions

Published on 26 Mar 2026 - 1:25

score 307 · Answer 7 · 2026-03-26 01:28:10

307

Views

Prove that the Hamming distances between three n-tuples cannot be 6,2,7

Published on 26 Mar 2026 - 1:28

score 347 · Answer 8 · 2026-03-26 04:35:09

347

Views

Irreducibility of $x^4 + x^3 + 1$ over finite field $\mathbb{F}_{2^{a}}$, $1 \leq a \leq 6$

Published on 26 Mar 2026 - 4:35

score 116 · Answer 9 · 2026-03-26 04:35:01

116

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If $\deg\left(f\right) = \min\left(\left\{d \in \mathbb{N}^\times;\; f\vert X^{q^d} - X\right\}\right)\,$, then $f$ is irreducible.

Published on 26 Mar 2026 - 4:35

score 89 · Answer 10 · 2026-03-26 04:34:55

89

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Why we ignore the other elements of $F_{p^k}$ when we check if any element of it is a root of multiplicity greater than $1$ in $p(x)$ or not?

Published on 26 Mar 2026 - 4:34

score 38 · Answer 11 · 2018-11-21 06:31:58

38

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How does the element of the field $F_{p^4}$ look like? Can I say it will look like $ [\theta , a , a^2 ,...., a^{(p^4 -1)} = 1]$

Published on 21 Nov 2018 - 6:31

score 300 · Answer 12 · 2018-11-21 08:10:35

300

Views

How can I prove that $(x^3-y^2)$ is a radical ideal in $\mathbb{F}_2[x,y]$?

Published on 21 Nov 2018 - 8:10

score 41 · Answer 13 · 2026-03-26 04:32:27

41

Views

multiplication of polynomials in $\mathbb{F}_2[x]$

Published on 26 Mar 2026 - 4:32

score 103 · Answer 14 · 2026-03-26 06:03:03

103

Views

Can this algorithm be fixed?

Published on 26 Mar 2026 - 6:03

score 183 · Answer 15 · 2018-11-23 07:24:22

183

Views

Prove $V$ over finite field of $q$ elements can be written as union of $q + 1$ proper subspaces

Published on 23 Nov 2018 - 7:24

List Question

Galois group of finite field extension

Nullity of the same matrix over a finite and infinite field

Definition of the d-th power residue symbol

$N$ random points make a random polynomial?

Multiplicative inverse of a polynomial in $GF(8)$

Finding the number of roots of u(X,Y) under certain restrictions

Prove that the Hamming distances between three n-tuples cannot be 6,2,7

Irreducibility of $x^4 + x^3 + 1$ over finite field $\mathbb{F}_{2^{a}}$, $1 \leq a \leq 6$

If $\deg\left(f\right) = \min\left(\left\{d \in \mathbb{N}^\times;\; f\vert X^{q^d} - X\right\}\right)\,$, then $f$ is irreducible.

Why we ignore the other elements of $F_{p^k}$ when we check if any element of it is a root of multiplicity greater than $1$ in $p(x)$ or not?

How does the element of the field $F_{p^4}$ look like? Can I say it will look like $ [\theta , a , a^2 ,...., a^{(p^4 -1)} = 1]$

How can I prove that $(x^3-y^2)$ is a radical ideal in $\mathbb{F}_2[x,y]$?

multiplication of polynomials in $\mathbb{F}_2[x]$

Can this algorithm be fixed?

Prove $V$ over finite field of $q$ elements can be written as union of $q + 1$ proper subspaces

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