Abstract
A basic problem about a constant dimension subspace code is to find its maximal possible size Aq(n, d, k). In this paper, we investigate constant dimension codes with parallel linkage construction and multilevel construction and obtain new lower bounds on Aq(18,6,9). By combining the Johnson type bound, we obtain new lower bounds on Aq(17,6,8). These lower bounds are larger than previously best known bounds in Heinlein et al. (2019).
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This article belongs to the Topical Collection: Boolean Functions and their Applications III
Guest Editors: Lilya Budaghyan, Claude Carlet, Tor Helleseth
This work was supported in part by National Natural Science Foundation of China (Nos. 61772015) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX20-0226).
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Niu, Y., Yue, Q. & Huang, D. New constant dimension subspace codes from parallel linkage construction and multilevel construction. Cryptogr. Commun. 14, 201–214 (2022). https://doi.org/10.1007/s12095-021-00504-z
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DOI: https://doi.org/10.1007/s12095-021-00504-z
Keywords
- Constant dimension codes
- Ferrers diagram
- Identifying vector
- Rank-metric codes
- Parallel linkage construction