Asymptotic bounds for spherical codes
- Autores: Manin Y.1, Marcolli M.2
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Afiliações:
- Max Planck Institute for Mathematics
- California Institute of Technology, Department of Mathematics
- Edição: Volume 83, Nº 3 (2019)
- Páginas: 133-157
- Seção: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133785
- DOI: https://doi.org/10.4213/im8739
- ID: 133785
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Resumo
The set of all error-correcting codes $C$ over a fixed finite alphabet$\mathbf{F}$ of cardinality $q$ determines the set of code points in the unit square $[0,1]^2$ with coordinates $(R(C), \delta (C))$:= (relative transmission rate, relative minimal distance). The central problemof the theory of such codes consists in maximising simultaneously the transmission rate of the code and the relative minimum Hamming distance between two different code words. The classical approach to this problem explored in vast literature consists in inventing explicit constructions of “good codes” and comparing new classes of codes with earlier ones.A less classical approach studies the geometry of the whole set of code points $(R,\delta)$ (with $q$ fixed), at first independently of its computability properties, and only afterwards turningto problems of computability, analogies with statistical physics, and so on.The main purpose of this article consists in extending this latter strategy to the domain of spherical codes.
Sobre autores
Yuri Manin
Max Planck Institute for MathematicsDoctor of physico-mathematical sciences
Matilde Marcolli
California Institute of Technology, Department of Mathematics
Email: matilde@caltech.edu
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