Pseudogeometries with clusters and an example of a recursive [4, 2, 3] 42 -code

In 1998, E. Couselo, S. Gonzalez, V. Markov, and A. Nechaev defined the recursive codes and obtained some results that allowed one to conjecture the existence of recursive MDS-codes of dimension 2 and length 4 over any finite alphabet of cardinality q ∉ {2, 6}. This conjecture remained open only for q ∈ {14, 18, 26, 42}. It is shown in this paper that there exist such codes for q = 42. We used a new construction, that of pseudogeometry with clusters.