Solving Some Affine Equations over Finite Fields

02/12/2020
by   Sihem Mesnager, et al.
0

Let l and k be two integers such that l|k. Define T_l^k(X):=X+X^p^l+...+X^p^l(k/l-2)+X^p^l(k/l-1) and S_l^k(X):=X-X^p^l+...+(-1)^(k/l-1)X^p^l(k/l-1), where p is any prime. This paper gives explicit representations of all solutions in p^n to the affine equations T_l^k(X)=a and S_l^k(X)=a, a∈p^n. For the case p=2 that was solved very recently in <cit.>, the result of this paper reveals another solution.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/25/2019

Solutions of x^q^k+...+x^q+x=a in GF2^n

Though it is well known that the roots of any affine polynomial over a f...
research
01/04/2021

Complete solution over p^n of the equation X^p^k+1+X+a=0

The problem of solving explicitly the equation P_a(X):=X^q+1+X+a=0 over ...
research
12/29/2019

Solving X^q+1+X+a=0 over Finite Fields

Solving the equation P_a(X):=X^q+1+X+a=0 over finite field Q, where Q=p^...
research
10/01/2020

On two conjectures about the intersection distribution

Recently, S. Li and A. Pott<cit.> proposed a new concept of intersection...
research
07/26/2020

Computing zeta functions of large polynomial systems over finite fields

In this paper, we improve the algorithms of Lauder-Wan <cit.> and Harvey...
research
07/24/2020

On the Number of Affine Equivalence Classes of Boolean Functions

Let R(r,n) be the rth order Reed-Muller code of length 2^n. The affine l...
research
04/22/2023

Explicit Directional Affine Extractors and Improved Hardness for Linear Branching Programs

In a recent work, Gryaznov, Pudlák, and Talebanfard (CCC' 22) introduced...

Please sign up or login with your details

Forgot password? Click here to reset