We give a new description of the so-called hyperbolic codes from which the minimum distance and the generator matrix are easily determined.

Jul 27, 2021 · A hyperbolic code is an evaluation code that improves a Reed-Muller because the dimension increases while the minimum distance is not penalized.

classical binary Reed-Muller codes are hyperbolic codes. The description in [8] of the hyperbolic codes is based on order domain theory. From the theory in ...

In [5] Saints and Heegard considered a class of codes called hyperbolic cascaded Reed-Solomon codes which can be seen as an improvement of the generalized ...

We give a new description of the so-called hyperbolic codes from which the minimum distance and the generator matrix are easily determined.

A hyperbolic code is an evaluation code that improves a Reed–Muller code because the dimension increases while the minimum distance is not penalized.

Single-shot code — A 4D hyperbolic surface code can be decoded with the Hastings decoder [2] in time O ( n log ⁡ n ) and with a logical error scaling inverse ...

Oct 14, 2023 · A hyperbolic code is an evaluation code that improves a Reed–Muller code because the dimension increases while the minimum distance is not ...

Mar 2, 2017 · We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3%.

2D hyperbolic surface codes have an asymptotically constant encoding rate k / n with a distance scaling logarithmically with n when the surface is closed.