New Construction for Constant Dimension Subspace Codes via a Composite Structure

摘要

One of the most fundamental topics in subspace coding is to explore the maximal possible value A(q)(n, d, k) of a set of k-dimensional subspaces in F-q(n) such that the subspace distance satisfies d(S)(U, V) = dim(U+V)-dim(U boolean AND V) >= 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.