Construction of q-ary(n,M,d)-codes in PG(2,16)

Abstract

The goal of this paper was to study the applications of the projective plane PG (2, q) over a Galois field of order q in the projective q-ary (n, M, d) -code such that the parameters length of code n, the maximum value size code M, and the minimum distance d with the error-correcting e according to an incidence matrix have been calculated. Also, this research provides examples and theorems of links between the combinatorial structures and coding theory. The method of the research depends on the classification of the points and lines in PG (2, q).