Covering Grassmannian Codes: Bounds and Constructions

07/19/2022
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by   Bingchen Qian, et al.
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Grassmannian 𝒒_q(n,k) is the set of all k-dimensional subspaces of the vector space 𝔽_q^n. Recently, Etzion and Zhang introduced a new notion called covering Grassmannian code which can be used in network coding solutions for generalized combination networks. An Ξ±-(n,k,Ξ΄)_q^c covering Grassmannian code π’ž is a subset of 𝒒_q(n,k) such that every set of Ξ± codewords of π’ž spans a subspace of dimension at least Ξ΄ +k in 𝔽_q^n. In this paper, we derive new upper and lower bounds on the size of covering Grassmannian codes. These bounds improve and extend the parameter range of known bounds.

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