scholarly journals Self-orthogonal Codes over Fq + uFq and Fq + uFq + u 2Fq

2020 ◽  
Vol 13 (4) ◽  
pp. 873-892
Author(s):  
Lucky Erap Galvez ◽  
Rowena Alma Betty ◽  
Fidel Nemenzo
Keyword(s):  
Finite Field ◽  
Mass Formula ◽  
Finite Ring ◽  
Orthogonal Codes ◽  
Mass Formulas

In this paper, we establish a mass formula for Euclidean and Hermitian self-orthogonal codes over the finite ring Fq + uFq, where Fq is the finite field of order q and u2 = 0. We also establish a mass formula for Euclidean self-orthogonal codes over the finite ring Fq + uFq + u2Fq, with u3 = 0 and characteristic of Fq is odd. These mass formulas are used to give a classification of Euclidean and Hermitian self-orthogonal codes over F2 + uF2 and F3 + uF3 of small lengths.

QUANTUM CODES FROM CYCLIC CODES OVER FINITE RING

2009 ◽  
Vol 07 (06) ◽  
pp. 1277-1283 ◽  
Author(s):  
JIANFA QIAN ◽  
WENPING MA ◽  
WANGMEI GUO
Keyword(s):  
Finite Field ◽  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Finite Ring ◽  
New Method ◽  
Quantum Codes ◽  
Orthogonal Codes ◽  
Quantum Error

A new method to obtain self-orthogonal codes over finite field F2 is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F2 + uF2. As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F2 + uF2.

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

scholarly journals Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen

2016 ◽  
Vol 13 (4) ◽  
pp. 846-852
Author(s):  
Baghdad Science Journal
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Maximum Size ◽  
Cubic Curves ◽  
Projective Equivalence

Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.

scholarly journals TOWARDS A CLASSIFICATION OF FINITE FIELD THEORIES

1994 ◽  
Vol 09 (27) ◽  
pp. 2555-2567
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Field ◽  
Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Finiteness Conditions ◽  
Gauge Groups ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for gauge groups SU (n)(n>6) and a rather general particle content. It is shown that in the class of theories considered (149 different particle contents), only two models are able to fulfill the finiteness conditions. Only one of these is supersymmetric. For the nonsupersymmetric one the appropriate Yukawa couplings are constructed explicitly.

The classification of small weakly minimal sets. III: Modules

1988 ◽  
Vol 53 (3) ◽  
pp. 975-979 ◽  
Author(s):  
Steven Buechler
Keyword(s):  
Finite Field ◽  
Algebraic Closure ◽  
Morley Rank ◽  
Minimal Sets

AbstractTheorem A. Let M be a left R-module such that Th(M) is small and weakly minimal, but does not have Morley rank 1. Let A = acl(∅) ⋂ M and I = {r ∈ R: rM ⊂ A}. Notice that I is an ideal.(i) F = R/Iis a finite field.(ii) Suppose that a, b0,…,bn, ∈ M and . Then there are s, ri ∈ R, i ≤ n, such that sa + Σi≤nribi ∈ A and s ∉ I.It follows from Theorem A that algebraic closure in M is modular. Using this and results in [B1] and [B2], we obtainTheorem B. Let M be as in Theorem A. Then Vaught's conjecture holds for Th(M).

scholarly journals Classification of cubic surfaces with twenty-seven lines over the finite field of order thirteen

2017 ◽  
Vol 4 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Anton Betten ◽  
James W. P. Hirschfeld ◽  
Fatma Karaoglu
Keyword(s):  
Finite Field ◽  
Cubic Surfaces

scholarly journals Classification of Rings with Toroidal and Projective Coannihilator Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Abdulaziz M. Alanazi ◽  
Mohd Nazim ◽  
Nadeem Ur Rehman
Keyword(s):  
Commutative Ring ◽  
Principal Ideal ◽  
Undirected Graph ◽  
Finite Ring ◽  
Vertex Set

Let S be a commutative ring with unity, and a set of nonunit elements is denoted by W S . The coannihilator graph of S , denoted by A G ′ S , is an undirected graph with vertex set W S ∗ (set of all nonzero nonunit elements of S ), and α ∼ β is an edge of A G ′ S ⇔ α ∉ α β S or β ∉ α β S , where δ S denotes the principal ideal generated by δ ∈ S . In this study, we first classify finite ring S , for which A G ′ S is isomorphic to some well-known graph. Then, we characterized the finite ring S , for which A G ′ S is toroidal or projective.

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