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 au thor and in part are new. Using a starting code with R = 2 as a "seed" thes e constructions yield an infinite family of codes with the same covering ra dius. New infinite families of codes with R = 2 are obtained for all alphab ets of size q greater than or equal to 4 and all codimensions r greater tha n or equal to 3 with the help of the constructions described. The parameter s obtained are better than those of known codes. New estimates for some par tition parameters in earlier known constructions are used to design new cod e families. Complete caps and other saturated sets of points in projective geometry are applied as starting codes. A table of new upper hounds on the length function for q = 4. 5, 7, R = 2. and r less than or equal to 2 is in cluded.