Lifted Codes with Construction of Echelon-Ferrers for Constant Dimension Codes

Finding the highest possible cardinality, Aq(n,d;k), of the set of k-dimensional subspaces in Fqn, also known as codewords, is a fundamental problem in constant dimension codes (CDCs). CDCs find applications in a number of domains, including distributed storage, cryptography, and random linear network coding. The goal of recent research papers has been to establish Aq(n,d;k). We further improved the echelon-Ferrers construction with an algorithm, and enhanced the inserting construction by swapping specified columns of the generator matrix to obtain new lower bounds.