On 24- Duality
Claude Carlet · 1995
Abstruct- Recently the notion on binary codes called 24 -linearity was introduced. 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 24-linear code and its 24-dual is stronger than the standard formal duality and we deduce the weight enumerators of related generalized codes.