List questions from finite-fields

Published on 25 Mar 2026 - 18:53

856

Views

Cardinality of polynomial ring over a finite field

Published on 04 May 2020 - 12:28

70

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Splitting field over Z_2

Published on 26 Mar 2026 - 17:43

173

Views

Find the least prime $p$ such that $x^{22} + x^{21} + \cdots + x + 1$ irreducible over $F_p$.

Published on 05 May 2020 - 4:26

137

Views

Splitting fields of polynomials over finite fields of prime-power order

Published on 05 May 2020 - 4:27

77

Views

Degree of extension over finite fields with two elements having same degree irreducible

Published on 05 May 2020 - 6:20

22

Views

Modulus operation for polynomials over GF(2)

Published on 05 May 2020 - 14:46

80

Views

showing $x^4+x^2+x+1$ is reducible in $GF(81)=GF(3^4)$

Published on 30 Mar 2026 - 5:13

2.2k

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How are the addition and multiplication tables for $GF(4)$ constructed?

Published on 28 Mar 2026 - 9:45

89

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Degree of splitting field is either $1$ or $2$

Published on 06 May 2020 - 16:38

302

Views

Minimum weight of ternary Golay code in cyclic form

Published on 28 Mar 2026 - 9:54

713

Views

When are Hamming codes cyclic?

Published on 28 Mar 2026 - 9:43

491

Views

Unable to invert matrix on Galois Field, even though the matrix should be invertible by construction

Published on 10 May 2020 - 22:57

89

Views

Degree of Permutation Polynomials

Published on 11 May 2020 - 14:09

172

Views

If p (mod 4) = 3 and p is a Gaussian Prime. How to show that Z[i]/(p) is equal to GF(p^2)/(x^2+1)?

Published on 25 Mar 2026 - 12:49

List Question

Proof of sub field and polynomial ring

Cardinality of polynomial ring over a finite field

Splitting field over Z_2

Find the least prime $p$ such that $x^{22} + x^{21} + \cdots + x + 1$ irreducible over $F_p$.

Splitting fields of polynomials over finite fields of prime-power order

Degree of extension over finite fields with two elements having same degree irreducible

Modulus operation for polynomials over GF(2)

showing $x^4+x^2+x+1$ is reducible in $GF(81)=GF(3^4)$

How are the addition and multiplication tables for $GF(4)$ constructed?

Degree of splitting field is either $1$ or $2$

Minimum weight of ternary Golay code in cyclic form

When are Hamming codes cyclic?

Unable to invert matrix on Galois Field, even though the matrix should be invertible by construction

Degree of Permutation Polynomials

If p (mod 4) = 3 and p is a Gaussian Prime. How to show that Z[i]/(p) is equal to GF(p^2)/(x^2+1)?

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