Results 11 to 20 of about 14,423,502 (287)
On the Automorphism Group of Polar Codes [PDF]
International Symposium on Information Theory, 2021 The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely ...
Marvin Geiselhart +4 more
semanticscholar +1 more source
The Complete Affine Automorphism Group of Polar Codes [PDF]
Global Communications Conference, 2021 Recently, a permutation-based successive cancellation (PSC) decoding framework for polar codes attracts much attention. It decodes several permuted codewords with indepen-dent successive cancellation (SC) decoders. Its latency thus can be reduced to that
Yuan Li +6 more
semanticscholar +1 more source
Group Properties of Polar Codes for Automorphism Ensemble Decoding [PDF]
IEEE Transactions on Information Theory, 2022 In this paper, we propose an analysis of the automorphism group of polar codes, with the aim of designing codes tailored for automorphism ensemble (AE) decoding.
Valerio Bioglio +2 more
semanticscholar +1 more source
The Stabilized Automorphism Group of a Subshift [PDF]
International mathematics research notices, 2020 For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic.
Yair Hartman, Bryna Kra, S. Schmieding
semanticscholar +1 more source
Reductivity of the automorphism group of K-polystable Fano varieties [PDF]
Inventiones Mathematicae, 2019 We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}
J. Alper +3 more
semanticscholar +1 more source
Calculating the virtual cohomological dimension of the automorphism group of a RAAG [PDF]
Bulletin of the London Mathematical Society, 2019 We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right‐angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis ...
M. Day, Andrew W. Sale, Richard D. Wade
semanticscholar +1 more source
On the automorphism group of a closed G2-structure [PDF]
Quarterly Journal of Mathematics, 2018 We study the automorphism group of a compact 7-manifold $M$ endowed with a closed non-parallel G$_2$-structure, showing that its identity component is abelian with dimension bounded by min$\{6,b_2(M)\}$.
F. Podestà, Alberto Raffero
semanticscholar +1 more source
The automorphism group of the universal Coxeter group [PDF]
Expositiones mathematicae, 2018 We study algebraic and geometric properties of the automorphism group of universal Coxeter group of rank $n\geq 4$, Aut$(W_n)$. In particular, we prove that whenever Aut$(W_n)$ acts by isometries on complete $d$-dimensional CAT(0) space with ...
Olga Varghese
semanticscholar +1 more source
Enriques surfaces with finite automorphism group in positive characteristic [PDF]
Algebraic Geometry, 2017 We classify Enriques surfaces with smooth K3 cover and finite automorphism group in arbitrary positive characteristic. The classification is the same as over the complex numbers except that some types are missing in small characteristics.
G. Martin
semanticscholar +1 more source
A surface with discrete and nonfinitely generated automorphism group [PDF]
Duke mathematical journal, 2017 We show that there is a smooth complex projective variety, of any dimension greater than or equal to two, whose automorphism group is discrete and not finitely generated.
T. Dinh, K. Oguiso
semanticscholar +1 more source