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Geometric approach to the MacWilliams Extension Theorem for codes over modules (1507.05212v1)
Published 18 Jul 2015 in cs.IT, math.CO, and math.IT
Abstract: The MacWilliams Extension Theorem states that each linear Hamming isometry of a linear code extends to a monomial map. In this paper an analogue of the extension theorem for linear codes over a module alphabet is observed. A geometric approach to the extendability of isometries is described. For a matrix module alphabet we found the minimum length of a code for which an unextendable Hamming isometry exists. We also proved an extension theorem for MDS codes over a module alphabet.