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On Z4-linear Preparata-like and Kerdock-like codes

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4 Author(s)
J. Borges ; Comput. Sci. Dept., Univ. Autonoma de Barcelona, Bellaterra, Spain ; K. T. Phelps ; J. Rifa ; V. A. Zinoviev

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 (1968) -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.

Published in:

IEEE Transactions on Information Theory  (Volume:49 ,  Issue: 11 )