Construction of subspace codes through linkage

Heide Gluesing-Luerssen; Carolyn  Troha

doi:10.3934/amc.2016023

Article Contents

2016, Volume 10, Issue 3: 525-540. Doi: 10.3934/amc.2016023

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Construction of subspace codes through linkage

Heide Gluesing-Luerssen^1, and
Carolyn Troha^2,

1.
University of Kentucky, Department of Mathematics, Lexington, KY 40506-0027
2.
Department of Mathematics, Viterbo University, La Crosse, WI

Received: May 2015

Revised: September 2015

Published: August 2016

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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.

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Mathematics Subject Classification: Primary: 11T71, 94B60; Secondary: 51E23.

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References

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