# Questions tagged [finite-fields]

The tag has no usage guidance.

14 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
244 views

### How is a "low-degree polynomial" precisely defined in Algebrization?

I'm going through papers which present algebrization as a barrier and I'm trying to understand how "low-degree" polynomials are precisely defined, i.e. are they low with respect to the ...
• 285
240 views

• 1,242
1 vote
68 views

### The curve used in Parvaresh-Vardy decoding

Consider the Parvaresh-Vardy list decoder. As I understand it, the idea is to decide on a curve over an extension field of the form $(f,f^h mod E, f^{h^2} mod E,\dots)$ and then evaluate each of ...
• 383
181 views

### Solving Linear Equations over finite field $Z_q$

Suppose we are given a linear equation $Ax=b$, where $A \in Z_q^{n \times m}$ and $b \in Z_q^n$. Note that $q$ is a prime here, and $Rank(A)= Rank(A;b)=n<m$. I wonder whether the ...
Let $F$ be a large finite field, where the elements are strings of length $n$. We require, addition, multiplication, and division to be efficient (polynomial in $n$). We say that $F$ is searchable if ...
### On permanent mod $3^t$ computation
By $'$ I mean transpose. I gather the info here from rjlipton.wordpress.com/2014/12/21/modulating-the-permanent. We know that if $U\in\Bbb F_{3^t}^{n\times n}$ satisfies $UU'=I_n$ in $\Bbb F_{3^t}$ ...