Properties of subspace subcodes of gabidulin codes

Abstract

We investigate properties of subspace subcodes of Gabidulin codes. They are isomorphic to Gabidulin codes with the same minimum rank dis- tance and smaller parameters. We design systematic encoding and decoding algorithms for subspace subcodes. We show that the direct sum of subspace subcodes of Gabidulin codes is isomorphic to the direct product of Gabidulin codes with smaller parameters. Thanks to this structure there is a great deal of correctable error-patterns whose rank exceeds the error-correcting capabil- ity. Finally we show that for particular sets of parameters, subfield subcodes of Gabidulin codes can be uniquely characterised by elements of the general linear group GLn(GF(q)) of non-singular q-ary matrices of size n. © 2008 AIMS-SDU.