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The rank and kernel of extended 1-perfect Z4-linear and additive non-Z4-linear codes

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

A binary extended 1-perfect code of length n + 1 = 2t is additive if it is a subgroup of Z2α × Z4β. The punctured code by deleting a Z2 coordinate (if there is one) gives a perfect additive code. 1-perfect additive codes were completely characterized and by using that characterization we compute the possible parameters α, β, rank, and dimension of the kernel for extended 1-perfect additive codes. A very special case is that of extended 1-perfect Z4-linear codes.

Published in:

Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 8 )

Date of Publication:

Aug. 2003

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