Affine Symplectic Grassmann codes
Fernando Pi\~nero Gonz\'alez, Doel Rivera Laboy

TL;DR
This paper introduces affine symplectic Grassmann codes, a new class of linear codes derived from affine parts of polar symplectic Grassmannians, analyzing their parameters, automorphisms, and duals.
Contribution
It defines a novel class of codes combining polar symplectic and affine Grassmann codes, and determines their key properties and parameters.
Findings
Determined code parameters and minimum distances.
Identified automorphism groups and dual codes.
Characterized minimum weight codewords.
Abstract
In this manuscript, we introduce a new class of linear codes, called affine symplectic Grassmann codes, and determine their parameters, automorphism group, minimum distance codewords, dual code and other key features. These linear codes are defined from an affine part of a polar symplectic Grassmannian. They combine polar symplectic Grassmann codes and affine Grassmann codes.
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Taxonomy
TopicsCooperative Communication and Network Coding · Coding theory and cryptography · Advanced Wireless Network Optimization
