Parameter-controlled inserting constructions of constant dimension subspace codes

08/23/2020

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by   Huimin Lao, et al.

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A basic problem in constant dimension subspace coding is to determine the maximal possible size A_q(n,d,k) of a set of k-dimensional subspaces in F_q^n such that the subspace distance satisfies dis(U,V)=2k-2(U ∩ V) ≥ d for any two different k-dimensional subspaces U and V in this set. In this paper we propose new parameter-controlled inserting constructions of constant dimension subspace codes. These inserting constructions are flexible because they are controlled by parameters. Several new better lower bounds which are better than all previously constructive lower bounds can be derived from our flexible inserting constructions. 141 new constant dimension subspace codes of distances 4,6,8 better than previously best known codes are constructed.