Emergent Mind
Geometric approach to the MacWilliams Extension Theorem for codes over modules
(1507.05212)
Published Jul 18, 2015
in
cs.IT
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math.CO
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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.
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