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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yongfeng Niu & Xuan Wang, 2024. "Lifted Codes with Construction of Echelon-Ferrers for Constant Dimension Codes," Mathematics, MDPI, vol. 12(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3270-:d:1501780
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