9415326 Sullivan This minority career advancement award supports mathematical research on applications of linear codes to organizing and classifying designs. The work focuses mainly on the mathematics of the codes themselves, less on the designs. Originally work of this type revolved around Steiner systems, in particular Steiner Triple and Quadruple systems and their corresponding binary codes. This work leads to consideration of weight-one vectors adjoined to the binary code of a projective geometry. It is conjectured that the new system is again a Steiner triple system. While this is expected to be worked out soon, there is further work to be done on the extension of this conjecture to extensions where more than one element is involved. Work will also be done on the question of whether all Steiner triple systems extend. This will be done by considering a relatively new class of designs, the Bagchi-Bagchi designs. ***
