New Constructions of Subspace Codes Using Subsets of MRD codes in Several Blocks

TL;DR

This paper introduces two novel methods for constructing constant dimension subspace codes using subsets of MRD codes, resulting in over 110 improved codes with better parameters than existing ones.

Contribution

The paper presents two new constructions of subspace codes utilizing subsets of MRD codes in multiple blocks, enhancing the known bounds for code sizes.

Findings

Over 110 new subspace codes constructed

New lower bounds for A_q(n, d, k) established

Improved code parameters over previous best known codes

Abstract

A basic problem for the constant dimension subspace coding is to determine the maximal possible size A_q (n, d, k) of a set of k-dimensional subspaces in Fnq such that the subspace distance satisfies d(U, V )> or =d for any two different subspaces U andV in this set. We present two new constructions of constant dimension subspace codes using subsets of maximal rank-distance (MRD) codes in several blocks. This method is firstly applied to the linkage construction and secondly to arbitrary number of blocks of lifting MRD codes. In these two constructions, subsets of MRD codes with bounded ranks play an essential role. The Delsarte theorem of the rank distribution of MRD codes is an important ingredient to count codewords in our constructed constant dimension subspace codes. We give many new lower bounds for A_q (n, d, k). More than 110 new constant dimension subspace codes better than previously best known codes are constructed.