Linear Codes and Polylinear Recurrences over Finite Rings and Modules
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Symplectic spread-based generalized Kerdock codes
Designs, Codes and Cryptography
| Hi-index | 754.84 |
Recently the notion on binary codes called Z4-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 Z4-linear code and its Z4 -dual is stronger than the standard formal duality and we deduce the weight enumerators of related generalized codes