Codes on Linear Sections of Grassmannians
Jes\'us Carrillo-Pacheco, Felipe Zald\'ivar
TL;DR
This paper explores algebraic geometry codes derived from linear sections of Grassmannian varieties, unifying several known classes like Schubert and Lagrangian-Grassmannian codes under this framework.
Contribution
It introduces a general approach to construct algebraic geometry codes from linear sections of Grassmannians, encompassing various special cases.
Findings
Schubert codes are instances of Grassmannian linear section codes.
Lagrangian-Grassmannian codes are included in this framework.
The approach links algebraic geometry with coding theory for new code constructions.
Abstract
We study algebraic geometry linear codes defined by linear sections of the Grassmannian variety as codes associated to FFN-projective varieties. As a consequence, we show that Schubert, Lagrangian-Grassmannian, and isotropic Grassmannian codes are special instances of codes defined by linear sections of the Grassmannian variety.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Advanced Algebra and Geometry