Making Auctions Work in Practice Is Worth a Nobel
Citation:
Kominers, Scott Duke. "Making Auctions Work in Practice Is Worth a Nobel." Bloomberg Opinion (October 12, 2020). View Details|
Article Journal de Théorie des Nombres de Bordeaux 2019 Configurations of Extremal Type II Codes via Harmonic Weight Enumerators |
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.
