scholarly journals Translation Hyperovals and $\mathbb{F}_2$-Linear Sets of Pseudoregulus Type

10.37236/8818 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Jozefien D'haeseleer ◽  
Geertrui Van de Voorde
Keyword(s):  
Finite Fields ◽  
Point Sets ◽  
Linear Set ◽  
Linear Sets ◽  
Even Order ◽  
Translation Ovals

In this paper, we study translation hyperovals in PG(2,qk). The main result of this paper characterises the point sets defined by translation hyperovals in the André/Bruck-Bose representation. We show that the affine point sets of translation hyperovals in PG(2,qk) are precisely those that have a scattered F2-linear set of pseudoregulus type in PG(2k−1,q) as set of directions. This correspondence is used to generalise the results of Barwick and Jackson who provided a characterisation for translation hyperovals in PG(2,q2), see [S.G. Barwick, Wen-Ai Jackson, A characterization of translation ovals in finite even order planes. Finite fields Appl. 33 (2015), 37--52.].

scholarly journals The characterization of elliptic curves over finite fields

1988 ◽  
Vol 45 (2) ◽  
pp. 275-286 ◽  
Author(s):  
J. W. P. Hirschfeld ◽  
J. F. Voloch
Keyword(s):  
Elliptic Curves ◽  
Finite Fields ◽  
Sufficient Conditions ◽  
Maximum Size ◽  
Desarguesian Plane ◽  
Cubic Curve ◽  
Odd Order ◽  
Even Order ◽  
Curves Over Finite Fields

AbstractIn a finite Desarguesian plane of odd order, it was shown by Segre thirty years ago that a set of maximum size with at most two points on a line is a conic. Here, in a plane of odd or even order, sufficient conditions are given for a set with at most three points on a line to be a cubic curve. The case of an elliptic curve is of particular interest.

The Characterization of Projections of Quadrics over Finite Fields of Even Order

1980 ◽  
Vol s2-22 (2) ◽  
pp. 226-238 ◽  
Author(s):  
J. W. P. Hirschfeld ◽  
J. A. Thas
Keyword(s):  
Finite Fields ◽  
Even Order

Approximation of Linear Sets in the Plane

2019 ◽  
Vol 7 (3) ◽  
pp. 60-69 ◽  
Author(s):  
В. Юрков ◽  
V. Yurkov
Keyword(s):  
Finite Number ◽  
Continuous Family ◽  
Point Sets ◽  
Multiple Points ◽  
Linear Set ◽  
Linear Sets ◽  
The Best Approximation ◽  
Special Factor ◽  
Almost All ◽  
The Given

A few general lines in the ordinary Euclidean plane are said to be line generators of a plane linear set. To be able to say that every line of the set belongs to one-parametrical line set we have to find their envelope. We thus create a pencil of lines. In this article it will be shown that there are a finite number of pencils in one linear set. To find a pencil of lines the linear parametrical approximation is applied. Almost all of problems concerning the parametrical approximation of figure sets are well known and deeply developed for any point sets. The problem of approximation for non-point sets is an actual one. The aim of this paper is to give a path to parametrical approximation of linear sets defined in plane. The sets are discrete and consist of finite number of lines without any order. Each line of the set is given as y = ax + b. Parametrical approximation means a transformation the discrete set of lines into completely continuous family of lines. There are some problems. 1. The problem of order. It is necessary to represent the chaotic set of lines as well-ordered one. The problem is solved by means of directed circuits. Any of chaotic sets has a finite number of directed circuits. To create an order means to find all directed circuits in the given set. 2. The problem of choice. In order to find the best approximation, for example, the simplest one it is necessary to choose the simplest circuit. Some criteria of the choice are discussed in the paper. 3. Interpolation the set of line factors. A direct approach would simply construct an interpolation for all line factors. But this can lead to undesirable oscillations of the line family. To eliminate the oscillations the special factor interpolation are suggested. There are linear sets having one or several multiple points, one or several multiple lines and various combinations of multiple points and lines. Some theorems applied to these cases are formulated in the paper.

scholarly journals A characterization of translation ovals in finite even order planes

2015 ◽  
Vol 33 ◽  
pp. 37-52 ◽  
Author(s):  
S.G. Barwick ◽  
Wen-Ai Jackson
Keyword(s):  
Even Order ◽  
Translation Ovals

scholarly journals Single Step 2-Port Device De-Embedding Algorithm for Fixture-DUT-Fixture Network Assembly

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1275
Author(s):  
Simone Scafati ◽  
Enza Pellegrino ◽  
Francesco de Paulis ◽  
Carlo Olivieri ◽  
James Drewniak ◽  
...  
Keyword(s):  
Standard Technique ◽  
Single Step ◽  
Scattering Parameters ◽  
Linear Set ◽  
S Parameter ◽  
Parameter Conversion ◽  
Before And After ◽  
One Step ◽  
Typical Measurement

The de-embedding of measurement fixtures is relevant for an accurate experimental characterization of radio frequency and digital electronic devices. The standard technique consists in removing the effects of the measurement fixtures by the calculation of the transfer scattering parameters (T-parameters) from the available measured (or simulated) global scattering parameters (S-parameters). The standard de-embedding is achieved by a multiple steps process, involving the S-to-T and subsequent T-to-S parameter conversion. In a typical measurement setup, two fixtures are usually placed before and after the device under test (DUT) allowing the connection of the device to the calibrated vector network analyzer coaxial ports. An alternative method is proposed in this paper: it is based on the newly developed multi-network cascading algorithm. The matrices involved in the fixture-DUT-fixture cascading gives rise to a non-linear set of equations that is in one step analytically solved in closed form, obtaining a unique solution. The method is shown to be effective and at least as accurate as the standard multi-step de-embedding one.

Characterization of nilpotent Lie algebras of breadth 3 over finite fields of odd characteristic

2021 ◽  
Author(s):  
Songpon Sriwongsa ◽  
Keng Wiboonton ◽  
Borworn Khuhirun
Keyword(s):  
Lie Algebras ◽  
Finite Fields ◽  
Nilpotent Lie Algebras

Characterization of Simple Symplectic Groups of Degree 4 over Locally Finite Fields in the Class of Periodic Groups

2018 ◽  
Vol 57 (3) ◽  
pp. 201-210
Author(s):  
D. V. Lytkina ◽  
V. D. Mazurov
Keyword(s):  
Finite Fields ◽  
Symplectic Groups ◽  
Locally Finite ◽  
Periodic Groups

Weighted Measures of Pseudorandom Binary Lattices

2021 ◽  
Vol 58 (3) ◽  
pp. 319-334
Author(s):  
Huaning Liu ◽  
Yinyin Yang
Keyword(s):  
Finite Fields ◽  
Lower Bounds ◽  
Binary Sequences ◽  
Quadratic Character ◽  
Pseudorandom Sequences ◽  
Even Order

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.

scholarly journals Characterization of Self-Adjoint Domains for Two-Interval Even Order Singular C-Symmetric Differential Operators in Direct Sum Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qinglan Bao ◽  
Xiaoling Hao ◽  
Jiong Sun
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Direct Sum ◽  
Even Order ◽  
Special Case ◽  
Symmetric Differential Operators

This paper is concerned with the characterization of all self-adjoint domains associated with two-interval even order singular C-symmetric differential operators in terms of boundary conditions. The previously known characterizations of Lagrange symmetric differential operators are a special case of this one.

scholarly journals A new characterization of collections of two-point sets with the uniqueness property

2007 ◽  
Vol 30 (2) ◽  
pp. 213-222
Author(s):  
Manabu Shirosaki
Keyword(s):  
Uniqueness Property ◽  
Point Sets
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