We say that a binary code of length n is additive if it is isomorphic to a subgroup of ℤ2α × ℤ4β, where the quaternary coordinates are transformed to binary by means of the usual Gray map and hence α + 2β = n. In this paper, we prove that any additive extended Preparata-like code always verifies α = 0, i.e., it is always a ℤ4-linear code. Moreover, we compute the rank and the dimension of the kernel of such Preparata-like codes and also the rank and the kernel of the ℤ4-dual of these codes, i.e., the ℤ4 -linear Kerdock-like codes.
|Journal||IEEE Transactions on Information Theory|
|Publication status||Published - 1 Nov 2003|
- Additive codes
- Kerdock code
- Preparata code
- ℤ -linear codes 4