Linear Recursive MDS-Codes and Asturian Codes

Let q = pt, where p is a prime. Then for any natural m, except the case m = 3 and q ≥ 8 is even, there exists a linear over the space Zpt m-dimensional recursive MDS-code of length q + 1 (q + 2 if q = m + 1 is even) which (in according to well-known conjecture of Bush, Blokhuis, Bruen & Thas) is believed to be the maximum of lengths of linear over the field GF(q) m-dimensional MDS-codes.