Constant-Rank Codes

Maximilien Gadouleau; Zhiyuan Yan

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arXiv · 0803.0778

Constant-Rank Codes

Maximilien Gadouleau·Zhiyuan Yan

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Abstract

Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random network coding. In this paper, we show that constant-rank codes are closely related to constant-dimension codes and we study the properties of constant-rank codes. We first introduce a relation between vectors in $\mathrm{GF}(q^m)^n$ and subspaces of $\mathrm{GF}(q)^m$ or $\mathrm{GF}(q)^n$, and use it to establish a relation between constant-rank codes and constant-dimension codes. We then derive bounds on the maximum cardinality of constant-rank codes with given rank weight and minimum rank distance. Finally, we investigate the asymptotic behavior of the maximal cardinality of constant-rank codes with given rank weight and minimum rank distance.

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Maximilien Gadouleau, Zhiyuan Yan. 2008-05-07. Constant-Rank Codes. https://arxiv.org/abs/0803.0778

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