Question

Irreducible polynomials of degree greater than 4 over finite fields

score 822 · Answer 1 · 2026-03-26 09:17:55

822

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Irreducible polynomials of degree greater than 4 over finite fields

Published on 26 Mar 2026 - 9:17

score 189 · Answer 2 · 2026-03-26 09:17:44

189

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Is $x^4 + 2x^2 - x + 1$ irreducible in $\mathbb Z_7[x]$?

Published on 26 Mar 2026 - 9:17

score 49 · Answer 3 · 2019-01-03 17:13:00

49

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Why $R/(a+bi)$ is a finite field with characteristic $p$ where $a^2+b^2=p$

Published on 03 Jan 2019 - 17:13

score 76 · Answer 4 · 2019-01-03 19:35:46

76

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irreducible polynomial has all its roots in $F_s$ and every element in $F_s$ satisfies such a polynomial

Published on 03 Jan 2019 - 19:35

score 74 · Answer 5 · 2026-03-25 23:53:12

74

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solutions of Differentially uniform mappings for cryptography

Published on 25 Mar 2026 - 23:53

score 28 · Answer 6 · 2019-01-04 13:42:46

28

Views

Let $F(x) \in GF(p)[x]$ a prime polynomial deg $n>0$, if $gcd(F,x^{q^i}-x)=1$ for $i=1,2,...,[n/2]$ $\iff$ $F$ is irreducible

Published on 04 Jan 2019 - 13:42

score 62 · Answer 7 · 2026-03-26 10:56:21

62

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Easy question about computing points of infinity

Published on 26 Mar 2026 - 10:56

score 107 · Answer 8 · 2026-03-22 17:16:35

107

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Convert from one tensor canonical form to another

Published on 22 Mar 2026 - 17:16

score 41 · Answer 9 · 2026-03-25 18:49:42

41

Views

Prove that if $p \not\equiv 1 \hspace{0.2 cm} (5)$ then $f(x) = x^{5} - 2$ has a unique solution in $\mathbb{F}_{p}$

Published on 25 Mar 2026 - 18:49

score 515 · Answer 10 · 2019-01-05 23:23:45

515

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Irreducible polynomial in $F[x]$ of degree $n$ is the minimal polynomial of exactly $n$ elements of $L$.

Published on 05 Jan 2019 - 23:23

score 413 · Answer 11 · 2026-03-24 23:46:46

413

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What does it mean that field $\mathbb{F}_{p^n}$ "contains" the prime field $\mathbb{Z}_p$?

Published on 24 Mar 2026 - 23:46

score 88 · Answer 12 · 2026-03-25 21:48:15

88

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Complement space of a finite dimensional space over a finite field

Published on 25 Mar 2026 - 21:48

score 723 · Answer 13 · 2026-03-22 12:09:06

723

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Can we find element of order $q^2-1$ in $\text{GL}_2(\mathbb{F}_q)$?

Published on 22 Mar 2026 - 12:09

score 320 · Answer 14 · 2026-03-26 09:19:44

320

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Generators of $\mathbb{Z}_2[x][x^3+x^2+1]$

Published on 26 Mar 2026 - 9:19

score 60 · Answer 15 · 2026-03-25 11:56:30

60

Views

Computing number of solutions for equations in $F_{m^s}$ (finite field with $m^s$ elements)

Published on 25 Mar 2026 - 11:56

List Question

Irreducible polynomials of degree greater than 4 over finite fields

Is $x^4 + 2x^2 - x + 1$ irreducible in $\mathbb Z_7[x]$?

Why $R/(a+bi)$ is a finite field with characteristic $p$ where $a^2+b^2=p$

irreducible polynomial has all its roots in $F_s$ and every element in $F_s$ satisfies such a polynomial

solutions of Differentially uniform mappings for cryptography

Let $F(x) \in GF(p)[x]$ a prime polynomial deg $n>0$, if $gcd(F,x^{q^i}-x)=1$ for $i=1,2,...,[n/2]$ $\iff$ $F$ is irreducible

Easy question about computing points of infinity

Convert from one tensor canonical form to another

Prove that if $p \not\equiv 1 \hspace{0.2 cm} (5)$ then $f(x) = x^{5} - 2$ has a unique solution in $\mathbb{F}_{p}$

Irreducible polynomial in $F[x]$ of degree $n$ is the minimal polynomial of exactly $n$ elements of $L$.

What does it mean that field $\mathbb{F}_{p^n}$ "contains" the prime field $\mathbb{Z}_p$?

Complement space of a finite dimensional space over a finite field

Can we find element of order $q^2-1$ in $\text{GL}_2(\mathbb{F}_q)$?

Generators of $\mathbb{Z}_2[x][x^3+x^2+1]$

Computing number of solutions for equations in $F_{m^s}$ (finite field with $m^s$ elements)

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