New Constant Dimension Subspace Codes From the Mixed Dimension Construction

One of the main problems of subspace coding is to determine the maximal size of a constant dimension subspace code with given parameters. In this paper, we show that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. We introduce a new class of subspace codes called mixed dimension/distance subspace codes. Using such codes, we present two constructions for large constant dimension subspace codes. The problem about the sizes of our constant dimension subspace codes is transformed into finding mixed dimension/distance subspace codes with large dimension distributions. The new constructed codes are the largest known for many sets of parameters. Our method gives at least 136 new lower bounds on the sizes of constant dimension subspace codes.