A simple proof of the formal duality of the Kerdock and Preparata codes
Zhexian, Wan · 中国科学通报：英文版 · 2000
The nonlinearity of the Z2-Kerdock code Km+1, where m is an odd integer ≥3, is not at all obvious. By regarding Km+1 as the binary image of the Z4-Kerdock code .,K(m) under the Gray map[1], a simple proof can be achieved (cf. Theorems 8.7 and 8.9 of [2]). Similarly, the formal duality of the Z2-Kerdock code Km+1 and the Z2-Preparata code Pm+1 is even more not at all obvious. A simple proof is given in the present note, by regarding Km+1 as the binary image of .K (m) and using the duality of .K(m) and the Z4-Preparata code . (m) established in [1].