An old conjecture about nonlinear codes resolved

The Kerdock codes and the Preparata codes are two families of binary nonlinear codes with parameters that suggest mutual duality. Even more so, their weight structures also satisfy a relation that normally is only met by linear codes that are each other's dual. Although these relations strongly suggest a deeper connection, leading researchers, after determining many inequivalent codes with the same parameters as the above named codes, came to believe that the apparent relation between them is purely coincidental. In 1994 two teams, Hammons-Kumar and Calderbank-Sloane-Solé, settled, independently of each other, the long-standing open problem of a possible relation in a very satisfactory way. Without going into all details, an impression of the history and solution of this open problem will be given