Designs, Codes and Cryptography

, Volume 85, Issue 2, pp 191–204 | Cite as

Cyclic subspace codes via subspace polynomials

Article

Abstract

Subspace codes have been intensely studied in the last decade due to their application in random network coding. In particular, cyclic subspace codes are very useful subspace codes with their efficient encoding and decoding algorithms. In a recent paper, Ben-Sasson et al. gave a systematic construction of subspace codes using subspace polynomials. In this paper, we mainly generalize and improve their result so that we can obtain larger codes for fixed parameters and also we can increase the density of some possible parameters. In addition, we give some relative remarks and explicit examples.

Keywords

Random network coding Subspace codes Constant dimension codes Grassmannian Cyclic subspace codes Subspace polynomials 

Mathematics Subject Classification

11T71 11T06 

Notes

Acknowledgments

We would like to thank the anonymous referees for their insightful and helpful comments that improved the presentation of this paper. In addition, we would like to thank COST Action IC 1104 and the first author thanks TÜBİTAK BİDEB 2211.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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