Geometric approach to the MacWilliams Extension Theorem for codes over modules
Information Theory
2017-05-29 v1 Combinatorics
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.
Cite
@article{arxiv.1507.05212,
title = {Geometric approach to the MacWilliams Extension Theorem for codes over modules},
author = {Serhii Dyshko},
journal= {arXiv preprint arXiv:1507.05212},
year = {2017}
}