# Questions tagged [finite-fields]

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39 questions
0answers
47 views

### Is linear algebra over $\mathbb{F}_2$ or a finite field possible? [closed]

I was interested in using Mathematica to do linear algebra over $\mathbb{F}_2$ in the context of solving for the code space of linear codes given a parity check matrix in $\mathbb{F}_2$. I've searched ...
1answer
170 views

### How to construct addition and multiplication table for finite field?

For example, choose $p(X) = X^4 + X + 1$, how to construct addition and multiplication tables for $\mathbb{F}_{2}[X] \mod{X^4 + X + 1}$ ?
1answer
61 views

### How to generate addition table for $GF(2)[x] \mod x^3 + 1 = 0$ [closed]

I have been playing with Mathematica for a while. I tried generating addition table for a simple ring $R$ such that $R = \mathbb{Z}_{15}$ as asked in my last question. However, I am completely ...
1answer
63 views

### How to generate addition table for ring $\mathbb Z_{15}$?

How do I generate an addition table for ring R such that $R = \mathbb{Z}_{15}$ or generally speaking, how to generate an addition table for any polynomial ring <...
1answer
62 views

### Plotting over a finite field

Is there a way to use a finite field for plotting functions in Mathematica? I couldn't find any options in the documentation.
0answers
93 views

### singular value decomposition of a matrix over a field K

Can I do singular value decomposition of a matrix which has entries from a field K, in my case $Z_m$, in Mathematica? For example, I have a matrix over a field Z2, with entries only 0 and 1. Using an ...
1answer
65 views

### What is the number of (binary) 4 x 4 matrices over GF(2) (the field with 2 elements) that do not have an eigenvalue of 0 or 1

My code below returns 4032. The OEIS sequence A002820 says there are 5824 such matrices. Is there something wrong with my code. I am assuming that the eigenvalues of a matrix are precisely the ...
1answer
137 views

### Checking matrix-invertibility in finite fields

Suppose the finite field $F=GF(2^d)$ contains all $p$-th roots of unity, where $p$ is a prime and $\omega\in F$ is the principal $p$-th root of unity. Let $V=(\omega^{ij})$ be a $p\times p$ ...
0answers
310 views

### How to compute the eigenvalue of a matrix over a finite field

How to compute the eigenvalue of a matrix over a finite field? I would like to compute the eigenvalues of the following matrix over $\mathbb F_5$. ...
2answers
135 views

### Construct Matrices from Coefficient of f[x] in Finite Fields?

I'm working on a problem at the moment using Mathematica and the Finite Fields package, and I've ran into some difficulty converting the problem to a Matrix, so I'm hoping somebody here would know how ...
1answer
158 views

### Matrix operations “Modulus->non-prime” problem

I am using Mathematica 10.4.1.0. When I specify the "Modulus" option to be a non-prime, the functions RowReduce and MatrixRank return the error ...
0answers
136 views

### display the elements of a quotient ring

How can I display the elements (polynomials) of the ring $$\mathbb Z_3[x]/\langle x^3+2x^2+1\rangle$$ Is there a built-in function that displays them?
1answer
115 views