Equireplicate balanced binary codes for oligo arrays (Q2753539)

A \((v,b,k,d)\)-balanced binary code (bbc) consists of a collection of \(b\) subsets, each of size \(k\), of a \(v\)-set, which is \(d\)-discriminated in that \(r_x\), the replication number for point \(x\), satisfies \(d\leq r_x\leq b-d\), for all \(x\), and that for any two distinct points, the number of blocks containing exactly one of them is at least \(d\). It is \(r\)-equireplicate if the replication number is \(r\) for every point. The authors have constructed such codes that are useful in the detection of defects in the manufacture of oligo arrays for DNA hybridization experiments. The stringent conditions needed for the existence of \(2\)-\((v,k,\lambda)\) block designs can be relaxed, allowing the construction of many additional bbc's that are useful in the application. Indeed, many such bbc's of interest have \(b< v\). The authors describe constructions of bbc's and provide much information on their existence for parameters within the range of practical interest.