# Minimum distance of linear codes and the α-invariant

@article{Garrousian2015MinimumDO,
title={Minimum distance of linear codes and the $\alpha$-invariant},
author={Mehdi Garrousian and Stefan O. Tohaneanu},
journal={ArXiv},
year={2015},
volume={abs/1507.03286}
}
• Published 13 July 2015
• Mathematics
• ArXiv
10 Citations
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This note shows that the methods used to find a lower bound for the minimal distance of complete intersection evaluation codes should apply to the case of (arithmetically) Gorenstein evaluation codes, and studies other lower bounds on the minimal Distance coming from the syzygies.
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Let ∆ be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C(∆) of rational functions generated by {1/α | α ∈ ∆}.