Subspace Codes in PG(2N − 1, Q)

Abstract

An (r,M,2δ;k)q constant-dimension subspace code, δ > 1, is a collection C of (k − 1)-dimensional projective subspaces of PG(r − 1,q) such that every (kδ)-dimensional projective subspace of PG(r − 1,q) is contained in at most one member of C. Constant-dimension subspace codes gained recently lot of interest due to the work by Koetter and Kschischang [20], where they presented an application of such codes for error-correction in random network coding. Here a (2n,M,4;n)q constant-dimension subspace code is constructed, for every n ≥ 4. The size of our codes is considerably larger than all known constructions so far, whenever n > 4. When n = 4 a further improvement is provided by constructing an (8,M,4;4)q constant-dimension subspace code, with M = q12 + q2(q2 + 1)2(q2 + q + 1) + 1.

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Correspondence to Antonio Cossidente.

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Cossidente, A., Pavese, F. Subspace Codes in PG(2N − 1, Q). Combinatorica 37, 1073–1095 (2017). https://doi.org/10.1007/s00493-016-3354-5

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Mathematics Subject Classification (2000)

  • 51E20
  • 05B25
  • 94B27
  • 94B60
  • 94B65