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Designs, Codes and Cryptography

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03-10-2022

Improved generalized block inserting construction of constant dimension codes

Authors: Xiaoqin Hong, Xiwang Cao

Published in: Designs, Codes and Cryptography | Issue 2/2023

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Abstract

Constant dimension codes (CDCs) have received extensive attention due to their applications in random network coding. The basic problem for CDCs is to determine the maximal possible cardinality \(A_q(n,d,k)\) of CDC for given parameters q, n, d and k. In this paper, we present some variations on the generalized block inserting construction method. These constructions insert more subspaces into the CDC from the parallel linkage construction via changing the parameters and shifting the positions of some small matrices. Our constructions help us to obtain CDCs with larger cardinalities and some new lower bounds for CDCs which are better than the previously best known ones.

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Title: Improved generalized block inserting construction of constant dimension codes
Authors: Xiaoqin Hong
Xiwang Cao
Publication date: 03-10-2022
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 2/2023
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-022-01117-0

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