• Corpus ID: 246016198

Generalized weights of codes over rings and invariants of monomial ideals

@inproceedings{Gorla2022GeneralizedWO,
  title={Generalized weights of codes over rings and invariants of monomial ideals},
  author={Elisa Gorla and Alberto Ravagnani},
  year={2022}
}
We develop an algebraic theory of supports for R-linear codes of fixed length, where R is a finite commutative unitary ring. A support naturally induces a notion of generalized weights and allows one to associate a monomial ideal to a code. Our main result states that, under suitable assumptions, the generalized weights of a code can be obtained from the graded Betti numbers of its associated monomial ideal. In the case of Fq-linear codes endowed with the Hamming metric, the ideal coincides… 

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