Optical orthogonal codes derived from difference triangle sets (Q2717913)

A family \(D_1,\ldots,D_n\) of subsets of \(Z_v\) with \(|D_i|=w\) for all \(i\) is called an optical orthogonal code if the list of differences \((d-d': d\neq d'\) and \(d, d'\in D_i\) for some \(i)\) covers every element of \(Z_v\) at most once. One may think of this as a generalization of cyclic Steiner systems where elements have to be covered precisely once. The authors describe a construction using difference triangle sets and additive sequences of permutations. The construction is illustrated with the case \(w=4\).