On the formal duals of Kerdock codes

Recently a new notion was introduced on binary codes, called Z₄-linearity, which explains why Kerdock codes and Delsarte-Goethals codes admit formal duals in spite of their nonlinearity. The “Z₄-duals” of these codes are new nonlinear codes which admit simpler decoding algorithms than the previously known formal duals. But their characterizations by means of algebraic equations are more complex. We give simpler algebraic characterizations of those codes. We next prove that the relationship between any Z₄-linear code and its Z₄-dual is stronger than the standard formal duality and deduce the weight enumerators of related generalized codes