Affine Hermitian Grassmann Codes
Fernando Pi\~nero Gonz\'alez, Doel Rivera Laboy
TL;DR
This paper introduces Affine Hermitian Grassmann Codes, a new class of linear codes derived from the affine parts of Polar Hermitian Grassmann codes, with determined parameters.
Contribution
It defines and analyzes a novel class of linear codes combining properties of Polar Hermitian and Affine Grassmann codes.
Findings
Parameters of Affine Hermitian Grassmann Codes are explicitly determined.
These codes merge features of Polar Hermitian and Affine Grassmann codes.
The study enhances understanding of algebraic geometric codes from Grassmannians.
Abstract
The Grassmannian is an important object in Algebraic Geometry. One of the many techniques used to study the Grassmannian is to build a vector space from its points in the projective embedding and study the properties of the resulting linear code. We introduce a new class of linear codes, called Affine Hermitian Grassman Codes. These codes are the linear codes resulting from an affine part of the projection of the Polar Hermitian Grassmann codes. They combine Polar Hermitian Grassmann codes and Affine Grassmann codes. We will determine the parameters of these codes.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Finite Group Theory Research