On the Classification of Type II Codes of Length 24

@article{Elkies2010OnTC,
  title={On the Classification of Type II Codes of Length 24},
  author={Noam D. Elkies and Scott Duke Kominers},
  journal={SIAM J. Discret. Math.},
  year={2010},
  volume={23},
  pages={2173-2177}
}
We give a new, purely coding-theoretic proof of Koch's criterion on the tetrad systems of Type II codes of length 24 using the theory of harmonic weight enumerators. This approach is inspired by Venkov's approach to the classification of the root systems of Type II lattices in $\mathbb{R}^{24}$ and gives a new instance of the analogy between lattices and codes. 
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