• DOI:10.1007/978-1-4614-7488-3_4
Corpus ID: 119170900

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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