Unidirectional covering codes

A code C⊆Zⁿ₂, where Z₂={0,1}, has unidirectional covering radius R if R is the smallest integer so that any word in Zⁿ₂ can be obtained from at least one codeword c∈C by replacing either 1s by 0s in at most R coordinates or 0s by 1s in at most R coordinates. The minimum cardinality of such a code is denoted by E(n,R). Upper bounds on this function are here obtained by constructing codes using tabu search; lower bounds, on the other hand, are mainly obtained by integer programming and exhaustive search. Best known bounds on E(n,R) for n≤13 and R≤6 are tabulated.