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  • 2019
  • Article
  • Journal de Théorie des Nombres de Bordeaux

Configurations of Extremal Type II Codes via Harmonic Weight Enumerators

By: Noam D. Elkies and Scott Duke Kominers
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Abstract

We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is generated by its codewords of minimal weight. Where Ozeki and Kominers used spherical harmonics and weighted theta functions, we use discrete harmonic polynomials and harmonic weight enumerators. Along the way we introduce "t12-designs" as a discrete analog of Venkov's spherical designs of the same name.

Keywords

Mathematical Methods

Citation

Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes via Harmonic Weight Enumerators." Journal de Théorie des Nombres de Bordeaux 31, no. 3 (2019): 679–688.
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About The Author

Scott Duke Kominers

Entrepreneurial Management
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  • Collusion in Brokered Markets By: John William Hatfield, Scott Duke Kominers and Richard Lowery
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  • O2X: Optimizing to the X By: Scott Duke Kominers, Thomas Jennings and Maisie Wiltshire-Gordon
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