GREYC, Université de Caen
INRIA, projet CODES
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.