Constructions and families of covering codes and saturated sets of points in projective geometry

In a recent paper by this author, constructions of linear binary covering codes are considered. In this work, constructions and techniques of the earlier paper are developed and modified for q-ary linear nonbinary covering codes, q 2 3, and new constructions are proposed. The described constructions design an infinite family of codes with covering radius R based on a starting code of the same covering radius. For arbitrary R 2 2, q 1 3, new infinite families of nonbinary covering codes with “good” parameters are obtained with the help of an iterative process when constructed codes are the starting codes for the following steps. The table of upper bounds on the length function for codes with q = 3, R = 2, 3, and codimension up to 24 is given. We propose to use saturated sets of points in projective geometries over finite fields as parity check matrices of starting codes. New saturated sets are obtained. Zndex Terms-Covering radius, covering codes, nonbinary codes, sat& rated sets of points in projective geometry, density of a covering.