From 17a7dddcbb2477c18555b2007d4baa469dcb6014 Mon Sep 17 00:00:00 2001
From: "Victor V. Albert" <valbert4@gmail.com>
Date: Thu, 9 Nov 2023 15:27:12 +1100
Subject: [PATCH] testability + 3d surface

---
 codes/classical/properties/ltc/ltc.yml                     | 2 +-
 .../classical/q-ary_digits/ag/generalized_reed_muller.yml  | 2 +-
 codes/classical/q-ary_digits/ltc/q-ary_ltc.yml             | 4 ++++
 .../topological/surface/higher_dim_surface/3d_surface.yml  | 7 ++++---
 .../qubits/subsystem/topological/3d_subsystem_surface.yml  | 5 ++++-
 5 files changed, 14 insertions(+), 6 deletions(-)

diff --git a/codes/classical/properties/ltc/ltc.yml b/codes/classical/properties/ltc/ltc.yml
index bf967903d..c85a49f66 100644
--- a/codes/classical/properties/ltc/ltc.yml
+++ b/codes/classical/properties/ltc/ltc.yml
@@ -17,7 +17,7 @@ description: |
   A technical definition for codes over binary alphabets is provided as follows; for general alphabets, see Ref. \cite{doi:10.1007/978-3-642-16367-8_6}.
   The idea behind LTCs is to be able to reliably test whether a given bit-string \(x\) is in the code by only sampling subsets of \(u\) bits.
   To have something to check against, we first have to define a collection of length-\(u\) subsets \(S\) of bit locations that are called \textit{allowed local views}.
-  A code is LTC if the following two conditions are satisfied \cite[Thm. 1.1]{arxiv:2111.04808}.
+  A code is an LTC if the following two conditions are satisfied \cite[Thm. 1.1]{arxiv:2111.04808}.
 
   First, if \(x\) is a codeword, then all of its restrictions \(x|_S\) to the subsets \(S\) are allowed local views,
   \begin{align}
diff --git a/codes/classical/q-ary_digits/ag/generalized_reed_muller.yml b/codes/classical/q-ary_digits/ag/generalized_reed_muller.yml
index e62525e64..d8e1e28d7 100644
--- a/codes/classical/q-ary_digits/ag/generalized_reed_muller.yml
+++ b/codes/classical/q-ary_digits/ag/generalized_reed_muller.yml
@@ -37,7 +37,7 @@ relations:
     - code_id: q-ary_cyclic
       detail: 'GRM codes with nonzero evaluation points are cyclic (\cite{doi:10.1007/978-94-011-3810-9}, pg. 52).'
     - code_id: q-ary_ltc
-      detail: 'GRM codes for \(r<q\) can be LTCs in the low- \cite{doi:10.1145/103418.103428,doi:10.1145/278298.278306} and high-error \cite{doi:10.1145/258533.258641,doi:10.1145/258533.258642} regimes.'
+      detail: 'GRM codes for \(r<q\) can be LTCs in the low- \cite{doi:10.1145/103418.103428,doi:10.1145/278298.278306} and high-error \cite{doi:10.1145/258533.258641,doi:10.1145/258533.258642} regimes. They admit weakly stable presentations of their correspoding groups \cite{arxiv:2311.04681}.'
     - code_id: group
       detail: 'GRM codes over prime-power fields are group-algebra codes \cite{doi:10.1007/BF01072842,manual:{Charpin, Pascale. Codes idéaux de certaines algèbres modulaires. Diss. 1982.},doi:10.1007/BF00141972}\cite[Ex. 16.4.11]{preset:HKSalgebra}.'
 
diff --git a/codes/classical/q-ary_digits/ltc/q-ary_ltc.yml b/codes/classical/q-ary_digits/ltc/q-ary_ltc.yml
index 582027a7a..13fd6bc6c 100644
--- a/codes/classical/q-ary_digits/ltc/q-ary_ltc.yml
+++ b/codes/classical/q-ary_digits/ltc/q-ary_ltc.yml
@@ -17,6 +17,10 @@ description: |
     \frac{1}{r}|H x| \geq \frac{R}{n} D(x,C)
   \end{align}
   holds for any \(q\)-ary string \(x\), where \(D(x,C)\) is the \(q\)-ary Hamming distance between \(x\) and the closest codeword to \(x\) \cite[Def. 11]{arxiv:1911.03069}.
+  A code satisfying the above constraint without the weight-\(u\) restriction is called an \(R\)\textit{-testable code} \cite{arxiv:2311.04681}.
+
+notes:
+  - 'Testable binary codes admit weakly stable presentations of their correspoding groups; this property is relevant to the disproof of the Connes embedding conjecture \cite{arxiv:2311.04681}.'
 
 relations:
   parents:
diff --git a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml
index a654bcf37..e7f7293c1 100644
--- a/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml
+++ b/codes/quantum/qubits/stabilizer/topological/surface/higher_dim_surface/3d_surface.yml
@@ -10,6 +10,9 @@ logical: qubits
 name: '3D surface code'
 introduced: '\cite{arxiv:quant-ph/0110143,arxiv:cond-mat/0411752}'
 
+alternative_names:
+  - '3D toric code'
+
 description: |
   A variant of the Kitaev surface code on a 3D lattice. The closely related \textit{solid code} \cite{arxiv:1406.4227} consists of several 3D surface codes stitched together in a way that the distance scales faster than the linear size of the system.
 
@@ -29,9 +32,7 @@ relations:
   parents:
     - code_id: higher_dimensional_surface
     - code_id: quantum_double_abelian
-  cousins:
-    - code_id: single_shot
-      detail: 'Some 3D surface codes are single-shot codes \cite{arxiv:2307.08118}.'
+
 
 # Begin Entry Meta Information
 _meta:
diff --git a/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml b/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml
index 6ac28ceec..d56b12776 100644
--- a/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml
+++ b/codes/quantum/qubits/subsystem/topological/3d_subsystem_surface.yml
@@ -10,6 +10,9 @@ logical: qubits
 name: '3D subsystem surface code'
 introduced: '\cite{arxiv:2106.02621}'
 
+alternative_names:
+  - '3D subsystem toric code'
+
 description: |
   Subsystem generalization of the surface code on a 3D cubic lattice with stabilizer generators of weight at most three.
 
@@ -18,7 +21,7 @@ relations:
   parents:
     - code_id: subsystem_stabilizer
     - code_id: single_shot
-      detail: 'The 3D subsystem surface code is a single-shot code \cite{arxiv:2106.02621,arxiv:2305.06365}.'
+      detail: 'The 3D subsystem surface code is a single-shot code \cite{arxiv:2106.02621,arxiv:2305.06365}; see Ref. \cite{arxiv:2307.08118} for an alternative formulation.'
   cousins:
     - code_id: 3d_surface
     - code_id: self_correct