Lower Bound for m3(2,37) and Related Code
Main Article Content
Abstract
In a finite projective plane PG(2, q), an (k, n)-arc is a set of k points of a projective plane such that some n, but no
n + 1 of them, are collinear. Here, the integer n is the degree of the arc and k ≥ n. The maximum size of an (k,n)-arc in
PG(2,q) is denoted by mn(2,q). In this paper the classification of the (k,3)-arcs in PG(2,37) is presented. It has been obtained
using a computer-based exhaustive search that exploits Secant distributions inequivalent (k,3)-arcs and produces exactly one
representative of each equivalence class. We established that 50 ≤ m3(2,37). The constructed (50,3)-arcs give the respective
lower bounds on m3(2,37). As a consequence there exist new three-dimensional linear codes over GF(37).
Downloads
Metrics
Article Details
Licensing
TURCOMAT publishes articles under the Creative Commons Attribution 4.0 International License (CC BY 4.0). This licensing allows for any use of the work, provided the original author(s) and source are credited, thereby facilitating the free exchange and use of research for the advancement of knowledge.
Detailed Licensing Terms
Attribution (BY): Users must give appropriate credit, provide a link to the license, and indicate if changes were made. Users may do so in any reasonable manner, but not in any way that suggests the licensor endorses them or their use.
No Additional Restrictions: Users may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
