Generalized linkage construction for constant-dimension codes
Daniel Heinlein
TL;DR
This paper introduces a generalized linkage construction for constant-dimension codes, improving existing methods and providing new lower bounds for their sizes, which were previously unknown.
Contribution
It extends and enhances two existing CDC constructions, resulting in a more versatile generalized linkage method that yields better bounds.
Findings
New generalized linkage construction for CDCs
Improved lower bounds for CDC cardinalities
Enhanced methods for constructing large CDCs
Abstract
A constant-dimension code (CDC) is a set of subspaces of constant dimension in a common vector space with upper bounded pairwise intersection. We improve and generalize two constructions for CDCs, the improved linkage construction and the parallel linkage construction, to the generalized linkage construction which in turn yields many improved lower bounds for the cardinalities of CDCs; a quantity not known in general.
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