Weighted Generating Functions for Type II Lattices and Codes

@article{Elkies2013WeightedGF,
  title={Weighted Generating Functions for Type II Lattices and Codes},
  author={N. Elkies and S. Kominers},
  journal={arXiv: Number Theory},
  year={2013},
  pages={63-108}
}
  • N. Elkies, S. Kominers
  • Published 2013
  • Mathematics
  • arXiv: Number Theory
  • We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we use the finite-dimensional representation theory of \(\mathfrak{s}\mathfrak{l}_{2}\) to derive a decomposition theorem for the spaces of discrete homogeneous polynomials in terms of the spaces of discrete harmonic polynomials, and… CONTINUE READING

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