Linear codes with covering radius 2 and other new covering codes

Infinite families of linear binary codes with covering radius R=2 and minimum distance d=3 and d=4 are given. Using the constructed codes with d=3, R=2, families of covering codes with R>2 are obtained. The parameters of many constructed codes with R<or=2 are better than the parameters of known codes. The parity check matrices of constructed codes with d=4, R=2 are equivalent to complete caps in projective geometry.<<ETX>>