The purpose of this article is to partition PG(3,11) into orbits. These orbits are studied from the view of caps using the subgroups of PGL(4,11) which are determined by nontrivial positive divisors of the order of PG(3,11). The τ_i-distribution and c_i-distribution are also founded for each cap.

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In this paper, the -caps are created by action of groups on the three-dimensional projective space over the Galois field of order eight. The types of -caps are also studied and determined either they form complete caps or not.

The principle objective in this paper is to computed the projectively inequivalent k-sets, k = 4, …,14 in the projective line P G(1,27) and then classified these k-set into (k − 1)-subsets and. Also, the group of projectivities of each k-set has been founded.

The aim of the paper is to compute projective maximum distance separable codes, -MDS of two and three dimensions with certain lengths and Hamming weight distribution from the arcs in the projective line and plane over the finite field of order twenty-five. Also, the linear codes generated by an incidence matrix of points and lines of  were studied over different finite fields.