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Network coding with flags

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Abstract

We develop a network coding technique based on flags of subspaces and a corresponding network channel model. To define error correcting codes we introduce a new distance on the flag variety, the Grassmann distance on flags and compare it to the commonly used gallery distance for full flags.

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References

  1. Abramenko P., Brown K.S.: Buildings Theory and Applications. Springer Graduate Texts in Mathematics, vol. 248. Springer, New York (2008).

  2. Ahlswede R., Cai N., Li S.-Y.R., Yeung R.W.: Network information flow. IEEE Trans. Inf. Theory 46, 1204–1216 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  3. Humphreys J.E.: Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics, vol. 29. Cambridge University Press, Cambridge (1990).

  4. Jones A.R.: A combinatorial approach to the double cosets of the symmetric group with respect to Young subgroups. Eur. J. Combin. 17, 647–655 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  5. Kötter R., Kschischang F.R.: Coding for errors and erasures in random network coding. IEEE Trans. Inf. Theory 54, 3579–3591 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  6. Petersen T.K., Tenner B.E.: The depth of a permutation. J. Combin. 6, 145–178 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  7. Silva D., Kschischang F.R., Kötter R.: A rank-metric approach to error control in random network coding. IEEE Trans. Inf. Theory 54, 3951–3967 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  8. Sloane N.J.A. (ed): The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org (2016). Accessed 31 May 2016.

  9. Taylor D.E.: The Geometry of the Classical Groups. Heldermann Verlag, Berlin (1992).

    MATH  Google Scholar 

  10. Vazquez-Castro M.A.: A geometric approach to dynamic network coding. In: IEEE Information Theory Workshop (2015).

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Acknowledgements

Dirk Liebhold is supported by the RTG 1632 of the DFG.

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Authors and Affiliations

  1. Lehrstuhl D für Mathematik, RWTH Aachen University, 52056, Aachen, Germany

    Dirk Liebhold & Gabriele Nebe

  2. Universitat Autonoma de Barcelona, Bellaterra, Spain

    Angeles Vazquez-Castro

Authors
  1. Dirk Liebhold
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  2. Gabriele Nebe
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  3. Angeles Vazquez-Castro
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Corresponding author

Correspondence to Gabriele Nebe.

Additional information

This is one of several papers published in Designs, Codes and Cryptography comprising the Special Issue on Network Coding and Designs.

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Liebhold, D., Nebe, G. & Vazquez-Castro, A. Network coding with flags. Des. Codes Cryptogr. 86, 269–284 (2018). https://doi.org/10.1007/s10623-017-0361-5

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  • DOI: https://doi.org/10.1007/s10623-017-0361-5

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