This article reviews some of the principal and recently-discovered lower and upper bounds
on the maximum size of (n, r)-arcs in PG (2, q), sets of n points with at most r points on a line …

We construct new (n, r)-arcs in PG (2, q) by prescribing a group of automorphisms and
solving the resulting Diophantine linear system with lattice point enumeration. We can …

International Electronic Journal of Geometry A NUMERICAL COMPUTATION OF (k, 3)-ARCS
IN THE LEFT SEMIFIELD PLANE OF ORDER 9 1. In Page 1 International Electronic Journal …

An arc of degree three is a set of points in projective plane no four of which are collinear but
some three are collinear, and a cubic curve is a non-singular projective plane cubic curve …

A cubic curve is a non-singular projective plane cubic curve. An (k; 3)-arc is a set of points
no four are collinear but some three are linear. Most of the cubic curve can be regarded as …

New good large (n,r)-arcs in PG(2,29) and PG(2,31) Page 1 ISSN 2148-838X https://doi.org/10.13069/jacodesmath.v11i2.267
J. Algebra Comb. Discrete Appl. 11(2) • 93–104 Received: 12 December 2022 Accepted: 30 …

ARAŞTIRMA MAKALESİ /RESEARCH ARTICLE Page 1 ANADOLU ÜNİVERSİTESİ BİLİM VE
TEKNOLOJİ DERGİSİ –B Teorik Bilimler ANADOLU UNIVERSITY JOURNAL OF SCIENCE …

The projective plane, PG (2; q), over a Galois field Fq is an incidence structure of points and
lines. A (k; n)-arc K in PG (2; q) is a set of k points such that no n+ 1 of them are collinear but …

Abstract A (k, r)-arc is a set of k points of a projective plane such that some r, but no r+ 1 of
them, are collinear. The maximum size of a (k, r)-arc in PG (2, q) is denoted by mr (2, q). In …

We construct linear codes over finite fields with prescribed minimum distance by selectiong
columns of the generator matrix. This selection problem can be formulated as an integer …