Designs, Codes and Cryptography

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

Cyclic subspace codes via subspace polynomials



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.


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

Mathematics Subject Classification

11T71 11T06 



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.


  1. 1.
    Ben-Sasson E., Etzion T., Gabizon A., Raviv N.: Subspace polynomials and cyclic subspace codes. IEEE Trans. Inf. Theory 62, 1157–1165 (2016).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Braun M., Etzion T., Ostergard P., Vardy A., Wasserman A.: Existence of q-analogues of Steiner systems. arXiv:1304.1462v2 [math.CO].
  3. 3.
    Drudge K.: On the orbits of Singer groups and their subgroups. Electron. J. Comb. 9(1), 10 (2002).MathSciNetMATHGoogle Scholar
  4. 4.
    Etzion T., Vardy A.: Error correcting codes in projective space. IEEE Trans. Inf. Theory 57, 1165–1173 (2011).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Gluesing-Luerssen H., Morrison K., Troha C.: Cyclic orbit codes and stabilizer subfields. Adv. Math. Commun. 25, 177–197 (2015).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Kohnert A., Kurz S.: Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance. In: Lecture Notes in Computer Science, vol. 5393, pp. 31–42, Springer, Berlin (2008).Google Scholar
  7. 7.
    Kötter R., Kschischang F.R.: Coding for errors and erasures in random network coding. IEEE Trans. Inf. Theory 54, 3579–3591 (2008).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Klein A., Metsch K., Storme L.: Small maximal partial spreads in classical finite polar spaces. Adv. Geom. 10, 379–402 (2010).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Lidl R., Niederreiter H.: Finite Fields. Encyclopedia of Mathematics and Its ApplicationsCambridge University Press, Cambridge (1997).MATHGoogle Scholar
  10. 10.
    Ore O.: On a special class of polynomials. Trans. Am. Math. Soc. 35, 559–584 (1933).MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Trautmann A.-L., Manganiello F., Braun M., Rosenthal J.: Cyclic orbit codes. IEEE Trans. Inf. Theory 59, 7386–7404 (2013).MathSciNetCrossRefMATHGoogle Scholar

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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