Merge branch 'main' of http://github.com/errorcorrectionzoo/eczoo_data

valbert4 · valbert4 · commit 0fba813de378 · 2026-05-22T09:26:29.000-04:00
diff --git a/codes/classical/bits/nonlinear/gray_map/duals/hergert.yml b/codes/classical/bits/nonlinear/gray_map/duals/hergert.yml
@@ -21,7 +21,7 @@ description: |
 
 features:
   decoders:
-    - 'Since the equivalent \(\mathbb{Z}_4\) codes are extended cyclic codes, efficient encoding and decoding is possible. \cite{arxiv:math/0207208,doi:10.1109/18.476333}.'
+    - 'Since the equivalent \(\mathbb{Z}_4\) codes are extended cyclic codes, efficient encoding and decoding is possible \cite{arxiv:math/0207208,doi:10.1109/18.476333}.'
 
 
 relations:
diff --git a/codes/classical/homogeneous/symmetric/2pt_homogeneous/complex_projective.yml b/codes/classical/homogeneous/symmetric/2pt_homogeneous/complex_projective.yml
@@ -14,7 +14,7 @@ alternative_names:
 
 
 description: |
-  Encodes \(K\) states (codewords) into a complex projective space \(\mathbb{C}P^N\), the space of lines in complex space. The space for \(N=2\) is called the complex projective plane.
+  Encodes \(K\) states (codewords) into a complex projective space \(\mathbb{C}P^N\), the space of lines in a complex vector space. The space for \(N=2\) is called the complex projective plane.
 
 
 notes:
diff --git a/codes/classical/q-ary_digits/distributed_storage/multiple_erasure_lrc/sequential_recovery.yml b/codes/classical/q-ary_digits/distributed_storage/multiple_erasure_lrc/sequential_recovery.yml
@@ -11,7 +11,7 @@ name: 'Sequential-recovery code'
 introduced: '\cite{arxiv:1401.2422,arxiv:1812.02502}'
 
 description: |
-  A \(t\)-erasure LRC whose coordinate erasures are recovered in sequential fashion.
+  A \(t\)-erasure LRC whose erased coordinates are recovered sequentially.
 
 
 relations:
diff --git a/codes/classical/q-ary_digits/distributed_storage/q-ary_lcc.yml b/codes/classical/q-ary_digits/distributed_storage/q-ary_lcc.yml
@@ -17,6 +17,7 @@ relations:
   parents:
     - code_id: q-ary_linear
     - code_id: lcc
+  cousins:
     - code_id: ldc
       detail: 'Linear LCCs can be converted into LDCs with the same locality \(r\) \cite[Sec. 2.4.1]{preset:Gopi18}.'
 
diff --git a/codes/classical/q-ary_digits/lexicographic.yml b/codes/classical/q-ary_digits/lexicographic.yml
@@ -13,7 +13,7 @@ introduced: '\cite{manual:{V. I. Levenshtein (1960). "A class of systematic code
 
 
 description: |
-  A \(q\)-ary code whose codewords are constructed greedily and iteratively by starting with zero and adding codewords whose distance is the desired minimum distance of the code.
+  A \(q\)-ary code whose codewords are constructed greedily and iteratively by starting with the all-zero word and adding codewords whose distance from all previously chosen codewords is at least the desired minimum distance of the code.
 
 relations:
   parents:
diff --git a/codes/classical/spherical/polytope/2d/polygon.yml b/codes/classical/spherical/polytope/2d/polygon.yml
@@ -10,7 +10,7 @@ logical: reals
 name: 'Polygon code'
 
 description: |
-  Spherical \((1,q,4\sin^2 \frac{\pi}{q})\) code for any \(q\geq1\) whose codewords are the vertices of a \(q\)-gon. Special cases include the line segment (\(q=2\)), triangle (\(q=3\)), square (\(q=4\)), pentagon (\(q=5\)), and hexagon (\(q=6\)).
+  Spherical \((1,q,4\sin^2 \frac{\pi}{q})\) code for any \(q\geq2\) whose codewords are the vertices of a \(q\)-gon. Special cases include the line segment (\(q=2\)), triangle (\(q=3\)), square (\(q=4\)), pentagon (\(q=5\)), and hexagon (\(q=6\)).
   
   \begin{figure}
     \includegraphics{polygon.svg}
diff --git a/codes/quantum/qubits/small_distance/small/7/xz_7_3_2.yml b/codes/quantum/qubits/small_distance/small/7/xz_7_3_2.yml
@@ -32,7 +32,7 @@ relations:
     - code_id: phantom
       detail: 'This code is the punctured version of the \([[8,3,2]]\) hypercube quantum code and is a phantom code \cite{arxiv:2601.20927}.'
     - code_id: quantum_reed_muller
-      detail: 'The punctured hypercube family is a binary quantum Reed-Muller family built from shortened and punctured classical Reed-Muller codes \cite{arxiv:2604.15111}.'
+      detail: 'The punctured hypercube family is a quantum Reed-Muller family built from shortened and punctured classical Reed-Muller codes \cite{arxiv:2604.15111}.'
     - code_id: small_distance_qubit_stabilizer
   cousins:
     - code_id: stab_8_3_2
diff --git a/codes/quantum/qubits/small_distance/small/8/stab_8_3_2.yml b/codes/quantum/qubits/small_distance/small/8/stab_8_3_2.yml
@@ -56,6 +56,10 @@ relations:
     - code_id: campbell_howard
       detail: 'The \([[8,3,2]]\) code is the \(k=1\) member of the \([[6k+2,3k,2]]\) Campbell-Howard family with a quasi-transversal logical \(CCZ\) gate \cite{arxiv:1606.01904}.'
   cousins:
+    - code_id: hamming844
+      detail: 'The \([[8,3,2]]\) hypercube code \(H_X\) check matrix is the parity-check matrix of the \([8,4,4]\) extended Hamming code, while its \(H_Z\) matrix is that of the SPC code.'
+    - code_id: parity_check
+      detail: 'The \([[8,3,2]]\) hypercube code \(H_X\) check matrix is the parity-check matrix of the \([8,4,4]\) extended Hamming code, while its \(H_Z\) matrix is that of the SPC code.'
     - code_id: xp_stabilizer
       detail: 'As the \(D=3\) member of the hypercube-code family, the \([[8,3,2]]\) code can be viewed as an XP stabilizer code with precision \(N=8\) \cite[Exam. 6.10]{arxiv:2203.00103}.'
     - code_id: stab_15_1_3
diff --git a/codes/quantum/qubits/stabilizer/qldpc/balanced_product/tensor/singlesector/hypergraph/quantum_expander.yml b/codes/quantum/qubits/stabilizer/qldpc/balanced_product/tensor/singlesector/hypergraph/quantum_expander.yml
@@ -31,10 +31,10 @@ features:
     - 'Dimensional jump protocols between various quantum expander codes \cite{arxiv:2510.06760}.'
 
   decoders:
-    - 'Small set-flip linear-time decoder, which corrects \hyperref[topic:asymptotics]{order} \(\Omega(n^{1/2})\) adversarial errors \cite{arxiv:1504.00822}. The decoder has been generalized to hypergraph products of 3 or more expander codes \cite{arxiv:2510.06760}'
+    - 'Small set-flip linear-time decoder, which corrects \hyperref[topic:asymptotics]{order} \(\Omega(n^{1/2})\) adversarial errors \cite{arxiv:1504.00822}. The decoder has been generalized to hypergraph products of 3 or more expander codes \cite{arxiv:2510.06760}.'
     - 'Log-time decoder \cite{arxiv:1808.03821}.'
     - 'Constant-time decoder \cite{manual:{A. Grospellier. Constant time decoding of quantum expander codes and application to fault-tolerant quantum computation. PhD thesis, Inria Paris (2019)}}.'
-    - '2D geometrically local syndrome extraction circuits acting on a patch of \(N\) physical qubits have to be of depth of \hyperref[topic:asymptotics]{order} \(\Omega(n/\sqrt{N})\) or deeper. More generally, there is a tradeoff between the depth \(D\) and width \(W\) of a syndrome extraction circuit, namely, \(D \geq n/\sqrt{W}\) \cite{arxiv:2109.14599}.'
+    - '2D geometrically local syndrome extraction circuits acting on a patch of \(N\) physical qubits must have depth of \hyperref[topic:asymptotics]{order} \(\Omega(n/\sqrt{N})\) or greater. More generally, there is a tradeoff between the depth \(D\) and width \(W\) of a syndrome extraction circuit, namely, \(D \geq n/\sqrt{W}\) \cite{arxiv:2109.14599}.'
 
   fault_tolerance:
     - 'Fault-tolerance with constant overhead can be achieved \cite{arxiv:1808.03821}.'
diff --git a/codes/quantum/qubits/stabilizer/qldpc/other_product/dlv.yml b/codes/quantum/qubits/stabilizer/qldpc/other_product/dlv.yml
@@ -15,7 +15,7 @@ description: |
   Member of a family of codes constructed using cubical chain complexes, which are \(t\)-order extensions of the complexes underlying expander codes (\(t=1\)) and expander lifted-product codes (\(t=2\)).
 
   For \(t=4\), assuming a conjecture about random linear maps, there exists a quantum locally testable family with linear dimension and inverse poly-logarithmic relative distance and soundness.
-  Applying weight reduction yields \hyperref[topic:asymptotics]{order} \(\Omega(1/\text{polylog}n)\) soundness, distance, and dimension, but \hyperref[topic:asymptotics]{order} \(\Theta(n)\) locality \cite[Table 4]{arxiv:2309.05541}.
+  Applying weight reduction yields \hyperref[topic:asymptotics]{order} \(\Omega(1/\text{polylog}n)\) soundness, \(\Omega(n/\text{polylog}n)\) distance and dimension, and constant locality \cite[Table 4]{arxiv:2309.05541}.
   Applying distance amplification and soundness amplification yields asymptotically constant soundness, \hyperref[topic:asymptotics]{order} \(\Theta(n)\) distance, \hyperref[topic:asymptotics]{order} \(\Theta(n)\) dimension, but poly-logarithmic locality \cite[Table 4]{arxiv:2309.05541}.
 
 
@@ -33,5 +33,7 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: GitHubCopilot
+      date: '2026-05-22'
     - user_id: VictorVAlbert
       date: '2024-02-13'
diff --git a/codes/quantum/qubits/subsystem/topological/color/2d_subsystem_color.yml b/codes/quantum/qubits/subsystem/topological/color/2d_subsystem_color.yml
@@ -18,7 +18,7 @@ description: |
   The original topological subsystem-code example is defined on the Union Jack lattice \cite{arxiv:0908.4246}; the square-octagon-lattice hypergraph construction of \cite{arxiv:1012.0425} reproduces the same code from a complementary viewpoint.
 
 protection: |
-  One family of subsystem codes has parameters \([[3m,2g,2m+2g-2,d]]\), where \(m\) is the number of vertices of the original embedded two-colex, where \(g\) is the genus of the surface embedding the two-colex, and where the distance is bounded from below by the length of the smallest nontrivial homological cycle of the two-colex \(\Gamma\) \cite[Construction B]{arxiv:1207.0479}\cite[Lemma 2]{arxiv:1805.12542}.
+  One family of subsystem codes has parameters \([[3m,2g,2m+2g-2,d]]\), where \(m\) is the number of vertices of the original embedded two-colex, \(g\) is the genus of the surface embedding the two-colex, and the distance is bounded from below by the length of the smallest nontrivial homological cycle of the two-colex \(\Gamma\) \cite[Construction B]{arxiv:1207.0479}\cite[Lemma 2]{arxiv:1805.12542}.
 
 
 
diff --git a/codes/quantum/qudits/qudits_into_qudits.yml b/codes/quantum/qudits/qudits_into_qudits.yml
@@ -15,7 +15,7 @@ alternative_names:
   - 'Modular-qudit subspace code'
 
 description: |
-  Encodes \(K\)-dimensional Hilbert space into a \(q^n\)-dimensional (\(n\)-qudit) Hilbert space, with canonical qudit states \(|k\rangle\) labeled by elements \(k\) of the group \(\mathbb{Z}_q\) of integers \textit{modulo} \(q\).
+  Encodes a \(K\)-dimensional Hilbert space into a \(q^n\)-dimensional (\(n\)-qudit) Hilbert space, with canonical qudit states \(|k\rangle\) labeled by elements \(k\) of the group \(\mathbb{Z}_q\) of integers \textit{modulo} \(q\).
   Usually denoted as \(((n,K))_{\mathbb{Z}_q}\) or \(((n,K,d))_{\mathbb{Z}_q}\), whenever the code's distance \(d\) is defined, and with \(q=p\) when the dimension is prime.
 
   There exists an analogue of the Wigner function for modular qudits \cite{arxiv:quant-ph/0401155,arxiv:quant-ph/0410117,arxiv:2503.09353}.
@@ -48,7 +48,7 @@ features:
   rate: 'Non-stabilizer states yield higher quantum capacity of the discrete beamsplitter channel \cite{arxiv:2401.12105}.'
   general_gates:
     - 'The normalizer of the \hyperref[topic:qudit-pauli]{modular-qudit Pauli group} is the \textit{modular-qudit Clifford group} \cite{arxiv:quant-ph/9802007,arxiv:quant-ph/0412001,arxiv:quant-ph/0408190,arxiv:quant-ph/0512155,arxiv:quant-ph/0605094,doi:10.1088/1751-8113/43/4/042001,arxiv:1101.1519,arxiv:1102.3354,arxiv:2008.00959}.
-    There is a standard form for modular-qudit Clifford-group operators \cite[Lemma 4]{arxiv:quant-ph/0412001}, and any modular-qudit gate can be constructed from phase-shift and quantum Fourier transform gates \cite{arxiv:1307.5087}.
+    There is a standard form for modular-qudit Clifford-group operators \cite[Lemma 4]{arxiv:quant-ph/0412001}, and any modular-qudit Clifford gate can be constructed from phase-shift and quantum Fourier transform gates \cite{arxiv:1307.5087}.
     Universal computing can be achieved using qudit Clifford gates and a single type of non-Clifford gate, such as the \(T\) gate \cite{arxiv:1503.08800}.
     Non-Clifford gates are typically more difficult to implement than Clifford gates and so are treated as a resource.
     There is a normal form for Clifford+\(T\) operators for qutrits \cite{arxiv:1803.03228} and, more generally, odd prime qudits \cite{arxiv:2011.07970}.
diff --git a/users/users_db.yml b/users/users_db.yml
@@ -104,6 +104,10 @@
 - user_id: AdamWills
   name: 'Adam Wills'
   gscholaruser: hyatxQ4AAAAJ
+
+- user_id: GitHubCopilot
+  name: 'GitHub Copilot'
+  githubusername: Copilot
   
 - user_id: BenjaminBrown
   name: 'Benjamin J. Brown'
