Lower bound for mr (2,41) and related code

Abstract

A (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. The maximum size of a (k, n) - arc in PG(2 q) is denoted by mr(2, q). In this paper we found mr(2,41) for n = (2,3 ,...,40) ,In this work, we construct a complete (k, n)-arcs in the projective space over Galois field GF(41), we construct the complete(k,n+1)-arcs from the complete (k, n)-arcs, where 2 ≤ n ≤ 42 , by using computer program we added some points of index zero, and found all the complete (k, n)-arcs in PG(2,41) and [k,n,d]_code.