On parameterized toric codes

2021 ◽  
Author(s):  
Esma Baran ◽  
Mesut Şahin
Keyword(s):  
Toric Codes

Non-split Toric Codes

2019 ◽  
Vol 55 (2) ◽  
pp. 124-144 ◽  
Author(s):  
D. I. Koshelev
Keyword(s):  
Toric Codes

scholarly journals Projecting three-dimensional color codes onto three-dimensional toric codes

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Arun B. Aloshious ◽  
Pradeep Kiran Sarvepalli
Keyword(s):  
Three Dimensional ◽  
Toric Codes

scholarly journals Reinforcement learning for optimal error correction of toric codes

2020 ◽  
Vol 384 (17) ◽  
pp. 126353 ◽  
Author(s):  
Laia Domingo Colomer ◽  
Michalis Skotiniotis ◽  
Ramon Muñoz-Tapia
Keyword(s):  
Reinforcement Learning ◽  
Error Correction ◽  
Optimal Error ◽  
Toric Codes

Projective toric codes

2021 ◽  
pp. 1-26
Author(s):  
Jade Nardi
Keyword(s):  
Error Correcting Code ◽  
Convex Polytope ◽  
Global Section ◽  
Explicit Construction ◽  
Geometric Error ◽  
Integral Points ◽  
Toric Codes ◽  
Algorithmic Technique ◽  
The One ◽  
Integral Convex Polytope

Any integral convex polytope [Formula: see text] in [Formula: see text] provides an [Formula: see text]-dimensional toric variety [Formula: see text] and an ample divisor [Formula: see text] on this variety. This paper gives an explicit construction of the algebraic geometric error-correcting code on [Formula: see text], obtained by evaluating global section of the line bundle corresponding to [Formula: see text] on every rational point of [Formula: see text]. This work presents an extension of toric codes analogous to the one of Reed–Muller codes into projective ones, by evaluating on the whole variety instead of considering only points with nonzero coordinates. The dimension of the code is given in terms of the number of integral points in the polytope [Formula: see text] and an algorithmic technique to get a lower bound on the minimum distance is described.

scholarly journals Toric codes and quantum doubles from two-body Hamiltonians

2011 ◽  
Vol 13 (5) ◽  
pp. 053039 ◽  
Author(s):  
Courtney G Brell ◽  
Steven T Flammia ◽  
Stephen D Bartlett ◽  
Andrew C Doherty
Keyword(s):  
Toric Codes

scholarly journals Small polygons and toric codes

2013 ◽  
Vol 51 ◽  
pp. 55-62 ◽  
Author(s):  
Gavin Brown ◽  
Alexander M. Kasprzyk
Keyword(s):  
Toric Codes

scholarly journals On the structure of generalized toric codes

2009 ◽  
Vol 44 (5) ◽  
pp. 499-506 ◽  
Author(s):  
Diego Ruano
Keyword(s):  
Toric Codes
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