New Construction for Constant Dimension Subspace Codes via a Composite Structure

One of the most fundamental topics in subspace coding is to explore the maximal possible value {\mathbf{A}}_{q}(n,d,k) of a set of k -dimensional subspaces in \mathbb F_{q}^{n} such that the subspace distance satisfies \text {d}_{\text {S}}(U,V) = \dim (U+V)-\dim (U\cap V)\,\,\geq d for any t...

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Bibliographic Details
Published in:IEEE communications letters 2021-05, Vol.25 (5), p.1422-1426
Main Authors: He, Xianmang, Chen, Yindong, Zhang, Zusheng, Zhou, Kunxiao
Format: Article
Language:English
Subjects:
Composite structures
constant dimension codes
Couplings
Encoding
Manufacturing
Measurement
MRD code
projective space
Subspace coding
Subspaces
Technology planning
Upper bound
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Summary:One of the most fundamental topics in subspace coding is to explore the maximal possible value {\mathbf{A}}_{q}(n,d,k) of a set of k -dimensional subspaces in \mathbb F_{q}^{n} such that the subspace distance satisfies \text {d}_{\text {S}}(U,V) = \dim (U+V)-\dim (U\cap V)\,\,\geq d for any two different k -dimensional subspaces U and V in this set. In this letter, we propose a construction for constant dimension subspace codes by inserting a composite structure composing of an MRD code and its sub-codes. Its vast advantage over the previous constructions has been confirmed through extensive examples. At least 49 new constant dimension subspace codes which exceeds the currently best codes are constructed.
ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2021.3052734