Advances in Mathematics of Communications (AMC)

Construction of subspace codes through linkage

Pages: 525 - 540, Volume 10, Issue 3, August 2016      doi:10.3934/amc.2016023

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Heide Gluesing-Luerssen - University of Kentucky, Department of Mathematics, Lexington, KY 40506-0027, United States (email)
Carolyn Troha - Department of Mathematics, Viterbo University, La Crosse, WI, United States (email)

Abstract: A construction is discussed that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting linkage code is as good as the minimum subspace distance of the constituent codes. As a special application, the construction of the best known partial spreads is reproduced. Finally, for a special case of linkage, a decoding algorithm is presented which amounts to decoding with respect to the smaller constituent codes and which can be parallelized.

Keywords:  Random network coding, constant dimension subspace codes, partial spreads.
Mathematics Subject Classification:  Primary: 11T71, 94B60; Secondary: 51E23.

Received: May 2015;      Revised: September 2015;      Available Online: August 2016.