Question

$E(\mathbb{F}_q ) \cong \mathbb{Z}/n \mathbb{Z}×\mathbb{Z}/n \mathbb{Z}$ implies $n|q-1$

score 62 · Answer 1 · 2026-03-28 13:28:09

62

Views

$E(\mathbb{F}_q ) \cong \mathbb{Z}/n \mathbb{Z}×\mathbb{Z}/n \mathbb{Z}$ implies $n|q-1$

Published on 28 Mar 2026 - 13:28

score 27 · Answer 2 · 2026-03-28 10:14:54

27

Views

Square root in $\mathbb F_{2^n}$

Published on 28 Mar 2026 - 10:14

score 34 · Answer 3 · 2026-03-26 21:12:26

34

Views

Find splitting field and irreducible decomposition

Published on 26 Mar 2026 - 21:12

score 47 · Answer 4 · 2020-06-08 13:50:09

47

Views

How does the polynomial $X^{p-1}+1$ split over $\mathbb{F}_p$

Published on 08 Jun 2020 - 13:50

score 180 · Answer 5 · 2026-03-28 13:22:52

180

Views

Prove that such a code does not exist

Published on 28 Mar 2026 - 13:22

score 99 · Answer 6 · 2026-03-31 12:15:59

99

Views

Polynomials of odd degree over $F_{p}$ have a root in $F_{p}$

Published on 31 Mar 2026 - 12:15

score 102 · Answer 7 · 2026-03-26 19:19:01

102

Views

Find decomposition of $x^8 -1$ over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_4$

Published on 26 Mar 2026 - 19:19

score 121 · Answer 8 · 2026-03-28 11:42:47

121

Views

Equivalence of two cyclic codes

Published on 28 Mar 2026 - 11:42

score 1k · Answer 9 · 2026-03-26 03:00:10

1k

Views

Schoof Algorithm : working on an example with SageMath

Published on 26 Mar 2026 - 3:00

score 40 · Answer 10 · 2020-06-12 11:11:24

Let $ \mathbb{K}$ be a field with 27 elements and $ a \in \mathbb{K}$. Then there exists $ x, y \in \mathbb{K}$ such that $ x^3 + y^5 = a$.

score 349 · Answer 11 · 2020-06-13 02:11:03

349

Views

Dimension of the field extension $F[x]/(f)=\deg(f)$ for an irreducible monic polynomial $f\in F[x]$

Published on 13 Jun 2020 - 2:11

score 136 · Answer 12 · 2026-03-28 11:42:18

136

Views

Show a code is cyclic given the generator matrix

Published on 28 Mar 2026 - 11:42

score 33 · Answer 13 · 2020-06-14 03:00:13

33

Views

When a finite extension $E$ of a finite prime field $F$ can be linear spaned by a subset of $E$?

Published on 14 Jun 2020 - 3:00

score 82 · Answer 14 · 2020-06-14 16:59:03

82

Views

The equation $x^2-x-1$ has no solution over finite fields of even order.

Published on 14 Jun 2020 - 16:59

score 52 · Answer 15 · 2026-03-26 04:35:10

52

Views

For $A \in F_2^{N \times M}$ find $\mathbf x \in F_2^M$ to maximize $L_0$ norm of $A \mathbf x$

Published on 26 Mar 2026 - 4:35

List Question

$E(\mathbb{F}_q ) \cong \mathbb{Z}/n \mathbb{Z}×\mathbb{Z}/n \mathbb{Z}$ implies $n|q-1$

Square root in $\mathbb F_{2^n}$

Find splitting field and irreducible decomposition

How does the polynomial $X^{p-1}+1$ split over $\mathbb{F}_p$

Prove that such a code does not exist

Polynomials of odd degree over $F_{p}$ have a root in $F_{p}$

Find decomposition of $x^8 -1$ over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_4$

Equivalence of two cyclic codes

Schoof Algorithm : working on an example with SageMath

Let $ \mathbb{K}$ be a field with 27 elements and $ a \in \mathbb{K}$. Then there exists $ x, y \in \mathbb{K}$ such that $ x^3 + y^5 = a$.

Dimension of the field extension $F[x]/(f)=\deg(f)$ for an irreducible monic polynomial $f\in F[x]$

Show a code is cyclic given the generator matrix

When a finite extension $E$ of a finite prime field $F$ can be linear spaned by a subset of $E$?

The equation $x^2-x-1$ has no solution over finite fields of even order.

For $A \in F_2^{N \times M}$ find $\mathbf x \in F_2^M$ to maximize $L_0$ norm of $A \mathbf x$

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