Differential Codes on Higher Dimensional Varieties Via Grothendieck's Residue Symbol
David Grant, John D. Massman, III, S. Srimathy
TL;DR
This paper introduces a novel method for constructing linear codes on higher dimensional varieties over finite fields by leveraging Grothendieck's residue theory, extending previous curve-based differential codes to more complex varieties.
Contribution
It generalizes the construction of differential codes from curves to higher-dimensional varieties using Grothendieck's residue symbol, offering a new approach in algebraic coding theory.
Findings
New construction method for codes on higher-dimensional varieties
Extension of differential codes from curves to varieties of higher dimension
Potential for improved code parameters and applications
Abstract
We give a new construction of linear codes over finite fields on higher dimensional varieties using Grothendieck's theory of residues. This generalizes the construction of differential codes over curves to varieties of higher dimensions.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Data Storage Technologies