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pro vyhledávání: '"11T06"'
Autor:
Da Conceição, Joaquim Cera
We consider the set of monic irreducible polynomials $P$ over a finite field $\mathbb{F}_q$ such that the multiplicative order modulo $P$ of some a in $\mathbb{F}_q(T)$ is divisible by a fixed positive integer $d$. Call $R_q(a,d)$ this set. We show t
Externí odkaz:
http://arxiv.org/abs/2412.09107
Autor:
Kapetanakis, Giorgos, Reis, Lucas
In 2022, S.D. Cohen and the two authors introduced and studied the concept of $(r, n)$-freeness on finite cyclic groups $G$ for suitable integers $r, n$, which is an arithmetic way of capturing elements of special forms that lie in the subgroups of $
Externí odkaz:
http://arxiv.org/abs/2412.07884
Autor:
Cheng, Kaimin
Let $p$ be a prime number and $q$ a power of $p$. Let $\fq$ be the finite field with $q$ elements. For a positive integer $n$ and a polynomial $\varphi(X)\in\fq[X]$, let $d_{n,\varphi}(X)$ denote the denominator of the $n$th iterate of $\frac{1}{\var
Externí odkaz:
http://arxiv.org/abs/2412.04985
Autor:
Ludhani, Rati
The Nullstellensatz, proved by Hilbert in 1893, is a classical result that holds when the base field is algebraically closed. When the base field is finite, a version of Hilbert's Nullstellensatz is given by Terjanian in 1966. Laksov in 1987 generali
Externí odkaz:
http://arxiv.org/abs/2411.06325
In this note we show (for a large enough dimension of the underlying field) a conjecture of [C. Beierle, C. Carlet, G. Leander, L. Perrin, {\em A further study of quadratic APN permutations in dimension nine}, Finite Fields Appl. 81 (2022), 102049] o
Externí odkaz:
http://arxiv.org/abs/2410.23097
In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding $f(X)=X^{q(p-1)+1} +\alpha X^{pq}+X^{q+p-1}$, on finite fields $\mathbb{F}_{q^2}, q=p^k$, from [A. R
Externí odkaz:
http://arxiv.org/abs/2410.22692
Autor:
Bary-Soroker, Lior, Shmueli, Roy
We study a random polynomial of degree $n$ over the finite field $\mathbb{F}_q$, where the coefficients are independent and identically distributed and uniformly chosen from the squares in $\mathbb{F}_q$. Our main result demonstrates that the likelih
Externí odkaz:
http://arxiv.org/abs/2410.16814
Autor:
Ehrenborg, Richard
Using the cyclotomic identity we compute sums over d-tuples of monic polynomials in F_q[x] weighted by the multiplicity of their irreducible factors. As consequences we determine explicit expressions for the number of d-tuples of polynomials such tha
Externí odkaz:
http://arxiv.org/abs/2410.12058
A function from $\Bbb F_{2^n}$ to $\Bbb F_{2^n}$ is said to be {\em $k$th order sum-free} if the sum of its values over each $k$-dimensional $\Bbb F_2$-affine subspace of $\Bbb F_{2^n}$ is nonzero. This notion was recently introduced by C. Carlet as,
Externí odkaz:
http://arxiv.org/abs/2410.10426
Autor:
Song, Yufeng, Luo, Jinquan
Projective Reed-Muller codes(PRM codes) are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. In this paper, we completely determine the minimal distance of the hull of any Projective Reed-Muller co
Externí odkaz:
http://arxiv.org/abs/2410.07217