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

Yongfeng Niu () and Xuan Wang
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Yongfeng Niu: School of Computer Science and Artificial Intelligence and Aliyun School of Big Data, Changzhou University, Changzhou 213100, China
Xuan Wang: School of Computer Science and Artificial Intelligence and Aliyun School of Big Data, Changzhou University, Changzhou 213100, China

Mathematics, 2024, vol. 12, issue 20, 1-12

Abstract: Finding the highest possible cardinality, A q ( n , d ; k ) , of the set of k -dimensional subspaces in F q n , 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 A q ( 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.

Keywords: constant dimension codes; linkage construction; greedy algorithm; echelon-Ferrers construction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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