New Constant-Dimension Subspace Codes from Maximum Rank Distance Codes
Liqing Xu, Hao Chen · IEEE Transactions on Information Theory · 2018
The main problem of constant-dimension subspace coding is to determine the maximal possible size Aq(n, d, k) of a set of k-dimensional subspaces in Fnq such that the subspace distance satisfies d(U, V) ≥ d for any two different subspaces U and V in this set. In this paper, we give a direct construction of constant-dimension subspace codes from two parallel versions of maximum rank-distance codes. The problem about the sizes of our constructed constant-dimension subspace codes is transformed into finding a suitable sufficient condition to restrict number of the roots of L1(L2(x)) - x where L1and L2are q-polynomials over the extension field Fqn. New lower bounds for Aq(4k, 2k, 2k), Aq(4k t 2, 2k, 2k t 1), and Aq(4k t 2, 2(k - 1), 2k t 1) are presented. Many new constantdimension subspace codes better than previously best known codes with small parameters are constructed.