On Z4-duality

Claude Carlet

GREYC, Université de Caen
BP 105
78153 Le Chesnay Cedex, France

IEEE Transactions on Information Theory, 41(5): 1487-1495, 1995.


Recently was introduced the new notion on binary codes called Z4-linearity. This notion explains why Kerdock codes and Delsarte-Goethals codes admit formal duals in spite of their nonlinearity. The "Z4-duals" of these codes (called 'Preparata' and 'Goethals' codes) are new nonlinear codes which admit simpler decoding algorithms than the previously known formal duals (the generalized Preparata and Goethals codes). We prove, by using the notion of exact weight enumerator, that the relationship between any Z4-linear code and its Z4-dual is stronger than the standard formal duality and we deduce the weight enumerators of related generalized codes.