Constructions, families, and tables of binary linear covering codes

Presents constructions and infinite families of binary linear covering codes with covering radii R=2,3,4. Using these codes, the authors obtain a table of constructive upper bounds on the length function l(r,R) for r⩽64 and R=2,3,4, where l(r, R) is the smallest length of a binary linear code with given codimension r and covering radius R. They obtain also upper bounds on l(r, R) for r=21, 28, R=5. Parameters of the constructed codes are better than parameters of previously known codes