2021/07/15 by Noémie C. Combe, Noemie Combe, Combe, Noemie +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #53D45 #62B10 #Cellular Automata and Applications #FOS: Computer and information sciences #Fractal and DNA sequence analysis #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #cs.IT #math.IT #msc:53D45 #msc:62B10
paper · pdf · doi:10.48550/arxiv.2107.07486
amstex, 42 pages
openalex publication_date 2021/07/15 · arxiv created 2022/03/02 · arxiv updated 2022/03/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Technology of data collection and information transmission is based on various mathematical models of encoding. The words "Geometry of information" refer to such models, whereas the words "Moufang patterns" refer to various sophisticated symmetries appearing naturally in such models. In this paper we show that the symmetries of spaces of probability distributions, endowed with their canonical Riemannian metric of information geometry, have the structure of a commutative Moufang loop. We also show that the F-manifold structure on the space of probability distribution can be described in terms of differential 3-webs and Malcev algebras. We then present a new construction of (noncommutative) Moufang loops associated to almost-symplectic structures over finite fields, and use then to construct a new class of code loops with associated quantum error-correcting codes and networks of perfect tensors.