Linear codes with covering radius R=2, 3 and codimension tR
Let [n, n - r](q)R denote a linear code over F-q with length n, codimension r, and covering radius R. We use a modification of constructions of [2q + 1, 2q - 3](q)2 and [3q + 1, 3q - 5](q)3 codes (q greater than or equal to 5) to produce infinite families of good codes with covering radius 2 and 3 and codimension tR.
linear code bounds on codes covering code lengthening projective geometry