On extendibility of additive code isometries

Abstract

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.