Generalized Hamming weights of affine Cartesian codes

Peter Beelen, Mrinmoy Datta*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Let F be any field and A1,…,Am be finite subsets of F. We determine the maximum number of common zeroes a linearly independent family of r polynomials of degree at most d of F[x1,…,xm] can have in A1×…×Am. In the case when F is a finite field, our results resolve the problem of determining the generalized Hamming weights of affine Cartesian codes. This is a generalization of the work of Heijnen and Pellikaan where these were determined for the generalized Reed–Muller codes. Finally, we determine the duals of affine Cartesian codes and compute their generalized Hamming weights as well.
Original languageEnglish
JournalFinite Fields and Their Applications
Volume51
Pages (from-to)130-145
ISSN1071-5797
DOIs
Publication statusPublished - 2018

Keywords

  • Data Processing
  • Algebra
  • Numerical Methods
  • Affine Cartesian codes
  • Affine Hilbert functions
  • Generalized Hamming weights
  • Zero dimensional varieties
  • Finite element method
  • Cartesians
  • Finite fields
  • Finite subsets
  • Generalized Hamming weight
  • Hilbert functions
  • Linearly independents
  • Zero-dimensional
  • Codes (symbols)

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