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2008, Volume 2, Issue 2: 147-157. Doi: 10.3934/amc.2008.2.147
This issue Previous Article The equivalence of space-time codes and codes defined over finite fields and Galois rings Next Article A combinatorial interpretation of double base number system and some consequences

Properties of subspace subcodes of Gabidulin codes

  • 1.

    Moscow Institute of Physics and Technology, Institutskii per. 9, 141700 Dolgoprudny, Moscow Region

  • 2.

    CELAR and IRMAR, Université de Rennes, La Roche Marguerite, BP 57419, 35171 Bruz

Received:  August 31, 2007
Revised:  January 31, 2008
Published:  April 2008
Abstract Related Papers Cited by
    Abstract
  • We investigate properties of subspace subcodes of Gabidulin codes. They are isomorphic to Gabidulin codes with the same minimum rank distance 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 capability. 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 GL$_n(GF(q))$ of non-singular $q$-ary matrices of size $n$.
    Mathematics Subject Classification: Primary: 11T71, 11T55; Secondary: 14G50.

    Citation:
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