scholarly journals On Lower Bounds for Incomplete Character Sums over Finite Fields

1996 ◽  
Vol 2 (2) ◽  
pp. 173-191 ◽  
Author(s):  
Ferruh Özbudak
1939 ◽  
Vol 71 (0) ◽  
pp. 99-121 ◽  
Author(s):  
H. Davenport
Keyword(s):  

2021 ◽  
Vol 58 (3) ◽  
pp. 319-334
Author(s):  
Huaning Liu ◽  
Yinyin Yang

In cryptography one needs pseudorandom sequences whose short subsequences are also pseudorandom. To handle this problem, Dartyge, Gyarmati and Sárközy introduced weighted measures of pseudorandomness of binary sequences. In this paper we continue the research in this direction. We introduce weighted pseudorandom measure for multidimensional binary lattices and estimate weighted pseudorandom measure for truly random binary lattices. We also give lower bounds for weighted measures of even order and present an example by using the quadratic character of finite fields.


2017 ◽  
Vol 46 ◽  
pp. 247-254 ◽  
Author(s):  
Abhishek Bhowmick ◽  
Thái Hoàng Lê ◽  
Yu-Ru Liu
Keyword(s):  

Author(s):  
Somphong Jitman ◽  
Aunyarut Bunyawat ◽  
Supanut Meesawat ◽  
Arithat Thanakulitthirat ◽  
Napat Thumwanit

A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary fieldF2. Over a nonbinary finite fieldFq, the set of good punctured polynomials of degree less than or equal to2are completely determined. Forn≥3, constructive lower bounds of the number of good punctured polynomials of degreenoverFqare given.


2015 ◽  
Vol 7 (2) ◽  
pp. 18
Author(s):  
Ali H. Hakami

Let $m$ be a positive integer with $m < p/2$ and $p$ is a prime. Let $\mathbb{F}_q$ be the finite field in $q = p^f$ elements, $Q({\mathbf{x}})$ be a nonsinqular quadratic form over $\mathbb{F}_q$ with $q$ odd, $V$ be the set of points in $\mathbb{F}_q^n$ satisfying the equation $Q({\mathbf{x}}) = 0$ in which the variables are restricted to a box of points of the type\[\mathcal{B}(m) = \left\{ {{\mathbf{x}} \in \mathbb{F}_q^n \left| {x_i  = \sum\limits_{j = 1}^f {x_{ij} \xi _j } ,\;\left| {x_{ij} } \right| < m,\;1 \leqslant i \leqslant n,\;1 \leqslant j \leqslant f} \right.} \right\},\]where $\xi _1 , \ldots ,\xi _f$ is a basis for $\mathbb{F}_q$ over $\mathbb{F}_p$ and $n > 2$ even. Set $\Delta  = \det Q$ such that $\chi \left( {( - 1)^{n/2} \Delta } \right) = 1.$ We shall motivate work of (Cochrane, 1986) to obtain lower bounds on $m,$ size of the box $\mathcal{B},$ so that $\mathcal{B} \cap V$ is nonempty. For this we show that the box $\mathcal{B}(m)$ contains a zero of $Q({\mathbf{x}})$ provided that $m \geqslant p^{1/2}.$ We also show that the box $\mathcal{B}(m)$ contains $n$ linearly independent zeros of $Q({\mathbf{x}})$ provided that $m \geqslant 2^{n/2} p^{1/2} .$


2016 ◽  
Vol 15 (07) ◽  
pp. 1650136 ◽  
Author(s):  
Ioulia N. Baoulina

We present a simple proof of the well-known fact concerning the number of solutions of diagonal equations over finite fields. In a similar manner, we give an alternative proof of the recent result on generalizations of Carlitz equations. In both cases, the use of character sums is avoided by using an elementary combinatorial argument.


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