On the kernel and rank of Z4-linear Preparata-like and Kerdock-like codes

J.Borges, K.T.Phelps, J.RifĂ , V.Zinoviev

Abstract. We say that a binary code of length n is additive if it is isomorphic to a subgroup of Z2a ×Z4b, where the quaternary coordinates are transformed to binary by means of the usual Gray map and hence a+2b = n.

In this paper we prove that any additive extended Preparata- like code always verifies a = 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.

Key words: Preparata Codes, Kerdock Codes, Kernel, Rank.

Registration: PIRDI-2/02, July 2002.

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Copyright © 2002 by Computer Science Department. UAB