2 research outputs found
MacWilliams Extension Theorem for MDS additive codes
The MacWilliams Extension Theorem states that each linear isometry of a
linear code extends to a monomial map. Unlike the linear codes, in general,
additive codes do not have the extension property. In this paper, an analogue
of the extension theorem for additive codes in the case of additive MDS codes
is proved. More precisely, it is shown that for almost all additive MDS codes
their additive isometries extend to isometries of the ambient space.Comment: 6 page
On extendibility of additive code isometries
For linear codes, the MacWilliams Extension Theorem states that each linear
isometry of a linear code extends to a linear isometry of the whole space. But,
in general, it is not the situation for nonlinear codes. In this paper it is
proved, that if the length of an additive code is less than some threshold
value, then an analogue of the MacWilliams Extension Theorem holds. One family
of unextendible code isometries for the threshold value of code length is
described.Comment: 11 page