A class of punctured simplex codes which are proper for error detection
  Binary linear [n,k] codes that are proper for error detection are known for many combinations of n and k. For the remaining combinations, existence of proper codes is conjectured. In this paper, a particular class of [n,k] codes is studied in detail. In particular, it is shown that these codes are proper for many combinations of n and k which were previously unsettled. 
Marco Baldi, Marco Bianchi, Franco Chiaraluce, Torleiv Kl{\o}ve
cs.IT math.IT