Constructions and families of nonbinary linear codes with covering radius 2

New constructions of linear nonbinary codes with covering radius R = 2 are proposed. They are in part modifications of earlier constructions by the author and in part are new. Using a starting code with R = 2 as a “seed” these constructions yield an infinite family of codes with the same covering radius. New infinite families of codes with R = 2 are obtained for all alphabets of size q 4 and all codimensions r 3 with the help of the constructions described. The parameters obtained are better than those of known codes. New estimates for some partition parameters in earlier known constructions are used to design new code families. Complete caps and other saturated sets of points in projective geometry are applied as starting codes. A table of new upper bounds on the length function for q = 4; 5; 7; R = 2; and r 24 is included.