Study subsets in Unite projective planes and their applications to Error-Correcting codes

Abstract

Abstract The main objective of this paper is to classify the special sets in the projective planes PG (2, t) with the values of t= 17,31,37, and we found the arcs of the second degree (k,2) - arcs in PG (2, t) or third-degree (k,3)-arcs in PG(2, t), and the parameters of codes n, k, d was calculated and whether they are complete or incomplete, and the corresponding codes were formed.