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Stanley–Reisner resolution of constant weight linear codes

Abstract

Given a constant weight linear code, we investigate its weight hierarchy and the Stanley–Reisner resolution of its associated matroid regarded as a simplicial complex. We also exhibit conditions on the higher weights sufficient to conclude that the code is of constant weight.

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Acknowledgments

We thank the anonymous referees for helpful remarks.

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Correspondence to Hugues Verdure.

Additional information

Communicated by T. Helleseth.

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Johnsen, T., Verdure, H. Stanley–Reisner resolution of constant weight linear codes. Des. Codes Cryptogr. 72, 471–481 (2014). https://doi.org/10.1007/s10623-012-9767-2

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Keywords

  • Constant weight
  • Linear code
  • Stanley–Reisner resolution
  • Betti numbers

Mathematics Subject Classification (2000)

  • 94B05
  • 05E45
  • 05B35
  • 13F55