haah <-> GB

errorcorrectionzoo · Oct 18, 2023 · e06edc8 · e06edc8
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diff --git a/codes/classical/properties/block/block.yml b/codes/classical/properties/block/block.yml
@@ -24,7 +24,7 @@ protection: |
   Block codes protect from errors acting on a few of the \(n\) symbols. A block code with \textit{distance} \(d\) detects errors acting on up to \(d-1\) symbols, and corrects erasure errors on up to \(d-1\) symbols.
 
 features:
-  rate: 'Ideal decoding error scales is suppressed exponentially with the number of subsystems \(n\), and the exponent has been studied in Ref. \cite{doi:10.1002/j.1538-7305.1959.tb03905.x,10.1016/S0019-9958(67)90052-6,manual:{Fano, Robert M. The transmission of information. Vol. 65. Cambridge, MA, USA: Massachusetts Institute of Technology, Research Laboratory of Electronics, 1949.}}.'
+  rate: 'Ideal decoding error scales is suppressed exponentially with the number of subsystems \(n\), and the exponent has been studied in Ref. \cite{doi:10.1002/j.1538-7305.1959.tb03905.x,doi:10.1016/S0019-9958(67)90052-6,manual:{Fano, Robert M. The transmission of information. Vol. 65. Cambridge, MA, USA: Massachusetts Institute of Technology, Research Laboratory of Electronics, 1949.}}.'
   decoders:
     - 'Decoding an error-correcting code is equivalent to finding the ground state of some statistical mechanical model \cite{doi:10.1038/339693a0}.'
 

diff --git a/codes/quantum/qubits/stabilizer/topological/fracton/haah_cubic.yml b/codes/quantum/qubits/stabilizer/topological/fracton/haah_cubic.yml
@@ -40,6 +40,8 @@ relations:
       detail: 'The color and cubic code families both include 3D codes that do not admit string-like operators.'
     - code_id: higher_dimensional_surface
       detail: 'The energy of any partial implementation of code 1 is proportional to the boundary length similar to the 4D toric code, which can potentially surpress the effects of thermal errors, but it is currently an open problem.'
+    - code_id: generalized_bicycle
+      detail: 'A GB code for the group \(G=\mathbb{Z}_3^{\times 3}\) is the cubic code \cite[Sec. III.A]{arXiv:2012.04068}.'
     - code_id: lifted_product
       detail: 'A lifted-product code for the ring \(R=\mathbb{F}_2[x,y,z]/(x^L-1,y^L-1,z^L-1)\) is the cubic code \cite[Appx. B]{arXiv:2111.03654}.'
 

diff --git a/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml b/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml
@@ -11,6 +11,9 @@ name: 'Two-block group-algebra (2BGA) codes'
 short_name: '2BGA'
 introduced: '\cite{arxiv:2305.06890,arXiv:2306.16400}'
 
+alternative_names:
+  - 'Non-Abelian GB code'
+
 description: |
   2BGA codes are the smallest \hyperref[code:lifted_product]{LP codes}
   LP\((a,b)\), constructed from a pair of \hyperref[topic:group-algebra]{group algebra} elements