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

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.

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.].

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.

Correction for “a Characterization of Finite Fields”

1967 ◽  
Vol 74 (10) ◽  
pp. 1211-1211
Author(s):  
Brother Joseph Heisler
Keyword(s):  
Finite Fields

A New Characterization of Semi-bent and Bent Functions on Finite Fields*

2006 ◽  
Vol 38 (2) ◽  
pp. 279-295 ◽  
Author(s):  
Khoongming Khoo ◽  
Guang Gong ◽  
Douglas R. Stinson
Keyword(s):  
Finite Fields ◽  
Bent Functions

scholarly journals A theorem on generation of finite orthogonal groups

1973 ◽  
Vol 16 (4) ◽  
pp. 495-506 ◽  
Author(s):  
W. J. Wong
Keyword(s):  
Finite Fields ◽  
Simple Groups ◽  
Symplectic Groups ◽  
Finite Simple Groups ◽  
Intermediate Result ◽  
Orthogonal Groups ◽  
Generators And Relations ◽  
Groups Of Lie Type

Presentation in terms of generators and relations for the classical finite simple groups of Lie type have been given by Steinberg and Curtis [2,4]. These presentations are useful in proving characterzation theorems for these groups, as in the author's work on the projective symplectic groups [5]. However, in some cases, the application is not quite instantaneous, and an intermediate result is needed to provide a presentation more suitable for the situation in hand. In this paper we prove such a result, for the orthogonal simple groups over finite fields of odd characteristic. In a subsequent article we shall use this to give a characterization of these groups in terms of the structure of the centralizer of an involution.

Large quartic groups on translation planes, II?Even order: Characterization of the Ott-Schaeffer planes

2005 ◽  
Vol 13 (3) ◽  
pp. 195-210
Author(s):  
Mauro Biliotti ◽  
Vikram Jha ◽  
Norman L. Johnson
Keyword(s):  
Translation Planes ◽  
Even Order
Sign in / Sign up

Export Citation Format

Share Document