MacWilliams Extension Theorem for MDS additive codes

摘要

The MacWilliams Extension Theorem states that each linear isometry of alinear code extends to a monomial map. Unlike the linear codes, in general,additive codes do not have the extension property. In this paper, an analogueof the extension theorem for additive codes in the case of additive MDS codesis proved. More precisely, it is shown that for almost all additive MDS codestheir additive isometries extend to isometries of the ambient space.