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Enhancing echelon-ferrers construction for constant dimension code

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Abstract

Echelon-Ferrers construction is one of the most powerful methods to improve the lower bounds for constant dimension codes. Although the method was proposed more than 10 years ago, it is still the best construction in a number of cases. In this paper, we remove parts of lifted FDRM codes from the echelon-Ferrers construction, and insert an SC-representation set, which finally improves the Echelon-ferrers construction, to get lower bounds for the following cases: \(A_q(11,4,4),\ A_q(15,4,4)\) and \(A_q(19,4,4)\).

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Acknowledgements

The work is partially supported by the National Natural Science Foundation of China (No. 61103244, 61672303, 61872083), the Science and Technology Planning Project of Guangdong Province (No. 190827105555406/2019ST032, 2019B010116001), the Natural Science Foundation of Guangdong Province (No. 2019A1515011123, 2020A1515010899), the Key Scientific Research Project of Universities in Guangdong Province (No. 2020ZDZX3028, 2020ZDZX3054), and the 2020 Li Ka Shing Foundation Cross-Disciplinary Research Grant (No. 2020LKSFG05D).

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Authors and Affiliations

  1. School of Cyberspace Security, Dongguan University of Technology, Dongguan, 526808, China

    Xianmang He, Zusheng Zhang & Jianguang Dun

  2. Department of Computer Science, Shantou University, Shantou, 515063, China

    Yindong Chen

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  1. Xianmang He
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  2. Yindong Chen
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  3. Zusheng Zhang
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  4. Jianguang Dun
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Correspondence to Yindong Chen.

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He, X., Chen, Y., Zhang, Z. et al. Enhancing echelon-ferrers construction for constant dimension code. J. Appl. Math. Comput. 68, 3767–3779 (2022). https://doi.org/10.1007/s12190-021-01680-0

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  • DOI: https://doi.org/10.1007/s12190-021-01680-0

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