• Corpus ID: 231740907

On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes

@article{Ghorpade2021OnTP,
  title={On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes},
  author={Sudhir R. Ghorpade and Rati Ludhani},
  journal={ArXiv},
  year={2021},
  volume={abs/2102.00308}
}
Following Johnsen and Verdure (2013), we can associate to any linear code C an abstract simplicial complex and in turn, a Stanley-Reisner ring RC . The ring RC is a standard graded algebra over a field and its projective dimension is precisely the dimension of C. Thus RC admits a graded minimal free resolution and the resulting graded Betti numbers are known to determine the generalized Hamming weights of C. The question of purity of the minimal free resolution of RC was considered by Ghorpade… 
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Generalized weights of codes over rings and invariants of monomial ideals

An algebraic theory of supports for R-linear codes of fixed length, where R is a finite commutative unitary ring, states that the generalized weights of a code can be obtained from the graded Betti numbers of its associated monomial ideal.

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