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

README.md

@@ -9,7 +9,7 @@ it!  Here's a BibTeX blurb you could use:
 ```bibtex
 @book{ErrorCorrectionZoo,
   title={The Error Correction Zoo},
-  year={2023},
+  year={2025},
   editor={Victor V. Albert and Philippe Faist},
   url={https://errorcorrectionzoo.org/}
 }

codes/classical/analog/lattice/points_into_lattices.yml

@@ -71,11 +71,10 @@ features:
 notes:
   - 'See books \cite{doi:10.1007/978-1-4757-6568-7,doi:10.1007/b98975} for introductions and overviews of lattices.'
   - 'See LMFDB \cite{manual:{The LMFDB Collaboration, The L-functions and modular forms database, https://www.lmfdb.org, 2024.}} and Catalogue of Lattices \cite{manual:{G. Nebe and N. J. A. Sloane. "Catalogue of Lattices." https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/index.html}} for databases of lattices.'
-  - 'Tables of bounds on kissing numbers \cite{manual:{H. Cohn. "Kissing numbers." https://cohn.mit.edu/kissing-numbers}}.'
+  - 'Tables of bounds on kissing numbers \cite{manual:{H. Cohn. "Kissing numbers." https://cohn.mit.edu/kissing-numbers}}. Popular summary of bounds on kissing numbers in 17-21 dimensions in \href{https://www.quantamagazine.org/mathematicians-discover-new-way-for-spheres-to-kiss-20250115/}{Quanta Magazine}.'
   - 'See Refs. \cite{manual:{Cannon, J., Bosma, W., Fieker, C., & Steel, A. (2008). HANDBOOK OF MAGMA FUNCTIONS.},doi:10.1145/190347.190362,doi:10.1006/jsco.1996.0125} for various examples and implementations in Magma.'
 
 
-
 relations:
   parents:
     - code_id: sphere_packing

codes/classical/bits/quantum_inspired/plaquette_ising.yml

@@ -0,0 +1,37 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: plaquette_ising
+physical: bits
+logical: bits
+
+name: 'Plaquette Ising code'
+introduced: '\cite{manual:{Ziman, John M. Models of disorder: the theoretical physics of homogeneously disordered systems. Cambridge university press, 1979.},arxiv:cond-mat/0309717,arxiv:cond-mat/0312587}'
+
+alternative_names:
+  - 'Right-angle water ice code'
+  - 'Xu-Moore code'
+# first Ziman, second is 2410.16250
+
+description: |
+  Classical code defined on a two-dimensional square lattice whose parity checks are applied on the four vertices of each square.
+  
+protection: |
+  The code has parameters \([L^2,2L-1,L]\) on a square lattice of size \(L\) \cite{arxiv:2410.16250}.
+
+relations:
+  parents:
+    - code_id: topological_classical
+  cousins:
+    - code_id: rotated_surface
+      detail: 'The plaquette Ising model can be thought of as the rotated surface code whose \(X\)-type stabilizer generators have been converted to \(Z\)-type stabilizer generators.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2025-01-16'

codes/classical/bits/reed_muller/reed_muller.yml

@@ -28,7 +28,7 @@ protection: |
   The \textit{Schwartz-Zippel Lemma} provides a distance lower bound on RM codes and extended the degree mantra from RS codes.
 
 features:
-  rate: 'Achieves capacity of the binary erasure channel \cite{arXiv:1505.05123,arXiv:1601.04689}, the binary memoryless symmetric (BMS) channel under bitwise maximum-a-posteriori decoding \cite{arxiv:2110.14631} (see also Ref. \cite{arxiv:1411.4590}), and the binary symmetric channel (BSC), solving a long-standing conjecture \cite{arxiv:2304.02509}.'
+  rate: 'Achieves capacity of the binary erasure channel \cite{arxiv:1505.05123,arxiv:1601.04689}, the binary memoryless symmetric (BMS) channel under bitwise maximum-a-posteriori decoding \cite{arxiv:2110.14631} (see also Ref. \cite{arxiv:1411.4590}), and the binary symmetric channel (BSC), solving a long-standing conjecture \cite{arxiv:2304.02509}.'
 
   decoders:
     - 'Reed decoder with \(r+1\)-step majority decoding corrects \(\frac{1}{2}(2^{m-r}-1)\) errors \cite{doi:10.1109/irepgelc.1954.6499441} (see also Ch. 13 of Ref. \cite{preset:MacSlo}).'

codes/classical/bits/tanner/ldpc.yml

@@ -54,6 +54,8 @@ notes:
   - 'See Encyclopedia of sparse graph codes for explicit representatives \cite{manual:{MacKay, David JC. "Encyclopedia of sparse graph codes." (2005).}}'
   - 'LDPC codes have been considered for quantum key distribution \cite{arxiv:2212.01121}.'
   - 'Codes have been benchmarked using AFF3CT toolbox \cite{doi:10.1016/j.softx.2019.100345}.'
+  - 'LDPC Python software package for decoding LDPC and QLDPC codes \cite{arxiv:2005.07016,manual:{Roffe, Joschka. "LDPC: Python tools for low density parity check codes." (2022).}}.'
+
 
 relations:
   parents:

codes/classical/properties/block/ecoc.yml

@@ -29,7 +29,7 @@ realizations:
 
 notes:
   - 'See \cite{doi:10.1109/TPAMI.2008.266}\cite[Ch. 6]{doi:10.1142/7238} for overviews of ECOCs.'
-  - 'See \cite{manual:{Escalera, Sergio, Oriol Pujol, and Petia Radeva. "Error-correcting ouput codes library." The Journal of Machine Learning Research 11 (2010): 661-664.}} for a library of ECOCs.'
+  - 'See \cite{manual:{Escalera, Sergio, Oriol Pujol, and Petia Radeva. "Error-correcting output codes library." The Journal of Machine Learning Research 11 (2010): 661-664.}} for a library of ECOCs.'
 
 
 relations:

codes/classical/properties/block/universally_optimal/t-designs.yml

@@ -29,19 +29,19 @@ description: |
   Such a design is called a \hyperref[code:combinatorial_design]{combinatorial design} (a.k.a. block design or covering design) \cite{manual:{Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973): vi+-97.}}, which includes Steiner systems as a special case.
   Designs on the full space of binary strings (Hamming space) are called \hyperref[code:orthogonal_array]{orthogonal arrays}.
 
-  More generally, designs exist when \(X\) is \(q\)-ary Hamming space, ordered Hamming space \cite{doi:10.4153/CJM-1999-017-5,arXiv:cs/0702033}, \(q\)-Johnson space \cite{manual:{Cameron, Peter J. "Generalisation of Fisher’s inequality to fields with more than one element." Combinatorics, London Math. Soc. Lecture Note Ser 13 (1973): 9-13.},doi:10.1145/2488608.2488715} (where they are called \hyperref[code:subspace_design]{subspace designs}), a sphere \cite{doi:10.1007/BF03187604} (where they are called \hyperref[code:spherical_design]{spherical designs}), or a compact connected two-point homogeneous space \cite{doi:10.1109/18.720545,preset:HPLevBounds,arXiv:1308.3188} (the sphere or the real, complex, quaternionic, or octonionic projective spaces \cite{doi:10.2307/1969427}).
+  More generally, designs exist when \(X\) is \(q\)-ary Hamming space, ordered Hamming space \cite{doi:10.4153/CJM-1999-017-5,arxiv:cs/0702033}, \(q\)-Johnson space \cite{manual:{Cameron, Peter J. "Generalisation of Fisher’s inequality to fields with more than one element." Combinatorics, London Math. Soc. Lecture Note Ser 13 (1973): 9-13.},doi:10.1145/2488608.2488715} (where they are called \hyperref[code:subspace_design]{subspace designs}), a sphere \cite{doi:10.1007/BF03187604} (where they are called \hyperref[code:spherical_design]{spherical designs}), or a compact connected two-point homogeneous space \cite{doi:10.1109/18.720545,preset:HPLevBounds,arxiv:1308.3188} (the sphere or the real, complex, quaternionic, or octonionic projective spaces \cite{doi:10.2307/1969427}).
 
-  Complex projective designs are designs on the space of all quantum states \cite{arXiv:quant-ph/0310075,arxiv:quant-ph/0701126,doi:10.1017/9781139207010}.
-  Symmetric informationally complete quantum measurements (SIC-POVMs) \cite{manual:{Zauner, G. (1999). Grundzüge einer nichtkommutativen Designtheorie. Ph. D. dissertation, PhD thesis.},arXiv:quant-ph/0310075} and mutually unbiased bases (MUBs) \cite{arxiv:quant-ph/0309120,arxiv:quant-ph/0502031,arxiv:0711.1017,arxiv:1004.3348,arxiv:1505.01123} are important examples of such designs.
+  Complex projective designs are designs on the space of all quantum states \cite{arxiv:quant-ph/0310075,arxiv:quant-ph/0701126,doi:10.1017/9781139207010}.
+  Symmetric informationally complete quantum measurements (SIC-POVMs) \cite{manual:{Zauner, G. (1999). Grundzüge einer nichtkommutativen Designtheorie. Ph. D. dissertation, PhD thesis.},arxiv:quant-ph/0310075} and mutually unbiased bases (MUBs) \cite{arxiv:quant-ph/0309120,arxiv:quant-ph/0502031,arxiv:0711.1017,arxiv:1004.3348,arxiv:1505.01123} are important examples of such designs.
   A limit of infinite dimensions yields rigged designs or, more colloquially, continuous-variable (CV) designs \cite{arxiv:2211.05127}, which can be used as operator-valued measures for the space of bosonic quantum states (i.e., Schwartz space over the reals).
 
   Designs also exist on groups.
-  Designs on the unitary (projective unitary) group are called strong unitary (unitary) designs \cite{arxiv:quant-ph/0512217,arxiv:quant-ph/0606161,arXiv:quant-ph/0611002}, while \(t\)-designs on the permutation group are called permutation \(t\)-designs \cite{doi:10.1017/S0963548300001917} (a.k.a. \(t\)-wise independent permutations).
+  Designs on the unitary (projective unitary) group are called strong unitary (unitary) designs \cite{arxiv:quant-ph/0512217,arxiv:quant-ph/0606161,arxiv:quant-ph/0611002}, while \(t\)-designs on the permutation group are called permutation \(t\)-designs \cite{doi:10.1017/S0963548300001917} (a.k.a. \(t\)-wise independent permutations).
 
-  Other notable designs include torus designs \cite{arXiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939,arxiv:1705.02978}, quantum-channel designs \cite{arxiv:2412.09672}, and designs on vertex operator algebras (a.k.a. conformal designs) \cite{arXiv:math/0701626}.
+  Other notable designs include torus designs \cite{arxiv:math/0405366,arxiv:2311.13479}, simplex designs \cite{doi:10.2307/2002483,doi:10.2307/2002484,doi:10.4036/iis.2018.S.02,doi:10.18434/M32189}, Grassmanian designs \cite{doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939,arxiv:1705.02978}, quantum-channel designs \cite{arxiv:2412.09672}, and designs on vertex operator algebras (a.k.a. conformal designs) \cite{arxiv:math/0701626}.
   Existence has been proven for combinatorial designs \cite{arxiv:1401.3665,doi:10.1016/0012-365X(87)90061-6,arxiv:1611.06827,arxiv:1802.05900,arxiv:2411.18291}, subspace designs \cite{doi:10.1016/j.jcta.2014.06.001,arxiv:2212.00870}, as well as designs on continuous topological spaces \cite{doi:10.1016/0001-8708(84)90022-7,arxiv:1111.5900,arxiv:1112.4900}.
 
-#  when restricted to act on distinct \(t\)-tuples; see \cite[Remarks 6-7]{arXiv:2404.14648}
+#  when restricted to act on distinct \(t\)-tuples; see \cite[Remarks 6-7]{arxiv:2404.14648}
 
 notes:
   - 'See books \cite{manual:{Stroud, Arthur H. Approximate calculation of multiple integrals. Prentice Hall, 1971.},doi:10.1201/9781420010541} for tables of various designs.'

codes/classical/q-ary_digits/ag/reed_solomon/rs/reed_solomon.yml

@@ -33,7 +33,7 @@ features:
     - '\([n,k,n-k+1]\) RS code requires an \hyperref[topic:asymptotics]{order} \(O(n^2)\) operations while encoding if a straightforward matrix multiplication is employed and \(k=O(n)\). Using the FFT algorithm, complexity of evaluating a polynomial at \(n\) roots of unity becomes \(O(n\log n)\). The FFT can be generalized to finite fields and rings, which is referred as Number-theoretic Transform (NTT). However, for some values of \(n\), which can not be factorized into small primes or do not have \(n\) roots of unity, the FFT algorithm fails. Independently developed by \cite{doi:10.1109/49.1926,doi:10.1016/0097-3165(89)90020-4} and generalized in Ref. \cite{doi:10.1017/CBO9781139856065}, the additive FFT solves this problem by evaluating the polynomial at \(n-1\) roots of unity when \(n\) is power of 2.'
 
   decoders:
-    - 'Decoding general RS codes is \(NP\)-hard \cite{arXiv:cs/0405005}.'
+    - 'Decoding general RS codes is \(NP\)-hard \cite{arxiv:cs/0405005}.'
     - 'Although using iFFT has its counterpart iNNT for finite fields, the decoding is usually standard polynomial interpolation in \(k=O(n\log^2 n)\). However, in erasure decoding, encoded values are only erased in \(r\) points, which is a specific case of polynomial interpolation and can be done in \(O(n\log n)\) by computing product of the received polynomial and an erasure locator polynomial and using long division to find an original polynomial. The long division step can be omitted to increase speed further by only dividing the derivative of the product polynomial, and derivative of erasure locator polynomial evaluated at erasure locations.'
     - 'Berlekamp-Massey decoder with runtime of \hyperref[topic:asymptotics]{order} \(O(n^2)\) \cite{doi:10.1109/TIT.1969.1054260,preset:Berlekamp}.'
     - 'Gorenstein-Peterson-Zierler decoder with runtime of \hyperref[topic:asymptotics]{order} \(O(n^3)\) \cite{doi:10.1109/TIT.1960.1057586,doi:10.1137/0109020} (see exposition in Ref. \cite{preset:Blahut}).'

codes/classical/q-ary_digits/alternative_metrics/insertion_deletion/dna.yml

@@ -14,7 +14,7 @@ description: |
   There exist several proposals tailored specifically for DNA storage \cite{arxiv:1410.8837,arxiv:1505.02199,doi:10.1038/s41598-017-05188-1,doi:10.1073/pnas.2004821117,doi:10.1109/TIT.2021.3066430}.
 
 protection: |
-  Noise affecting DNA molecules can include insertions and deletions \cite{arxiv:1803.03322}. The DNA data storage channel has been characterized \cite{arxiv:1410.8837,arxiv:1502.00517,arXiv:1803.03322}.
+  Noise affecting DNA molecules can include insertions and deletions \cite{arxiv:1803.03322}. The DNA data storage channel has been characterized \cite{arxiv:1410.8837,arxiv:1502.00517,arxiv:1803.03322}.
 
 notes:
   - 'Review of DNA-based coding \cite{arxiv:1507.01611}.'

codes/classical/q-ary_digits/alternative_metrics/poset/poset.yml

@@ -19,7 +19,7 @@ protection: |
   An ideal \(\langle \text{supp}(x) \rangle\) generated by \(x\in GF(q)^n\) contains all subsets of \([n]\) that are less than or equal to the subset in the support of \(x\) in the partial ordering.
   The \textit{poset metric} between two strings \(x,y\) is then the cardinality of the ideal generated by the difference between the supports of \(x\) and \(y\), \(d_P(x,y) = |\langle \text{supp}(x-y) \rangle|\).
 
-  Generalizations of various bounds for ordinary \(q\)-ary codes have been developed for poset codes, including generalizations of \hyperref[topic:weight-enumerator]{MacWilliams identities} \cite{arXiv:1205.1090}; see \cite{preset:HKSmetrics}.
+  Generalizations of various bounds for ordinary \(q\)-ary codes have been developed for poset codes, including generalizations of \hyperref[topic:weight-enumerator]{MacWilliams identities} \cite{arxiv:1205.1090}; see \cite{preset:HKSmetrics}.
 
 
 notes:

codes/classical/q-ary_digits/distributed_storage/multiple_erasure_lrc/parallel_recovery.yml

@@ -8,7 +8,7 @@ physical: q-ary_digits
 logical: q-ary_digits
 
 name: 'Parallel-recovery code'
-introduced: '\cite{arXiv:1302.5518}'
+introduced: '\cite{arxiv:1302.5518}'
 
 description: |
   A \(t\)-erasure LRC whose coordinate erasures can be recovered in parallel.

codes/classical/q-ary_digits/q-ary_linear.yml

@@ -28,7 +28,7 @@ protection: |
 
 
 features:
-  rate: 'Any code admitting a two-transitive automorphism group achieves capacity under the binary erasure channel \cite{arXiv:1505.05123,arXiv:1601.04689,arxiv:2010.15453}.'
+  rate: 'Any code admitting a two-transitive automorphism group achieves capacity under the binary erasure channel \cite{arxiv:1505.05123,arxiv:1601.04689,arxiv:2010.15453}.'
   decoders:
     - 'Maximum likelihood (ML) decoding. This algorithm decodes a received word to the most likely sent codeword based on the received word. ML decoding of reduced complexity is possible for virtually all \(q\)-ary linear codes \cite{doi:10.1109/ISIT.1997.613333}.'
     - 'Optimal symbol-by-symbol decoding rule \cite{doi:10.1109/TIT.1976.1055617}.'

codes/classical/spherical/q-ary/complex_hadamard.yml

@@ -18,7 +18,7 @@ protection: |
 
 
 notes:
-  - 'Database of complex Hadamard matrices \cite{arXiv:quant-ph/0512154}.'
+  - 'Database of complex Hadamard matrices \cite{arxiv:quant-ph/0512154}.'
 
 relations:
   parents:

codes/eacq.yml

@@ -30,7 +30,7 @@ protection: |
   The EA hybrid Singleton bound represents a triple trade-off region in the combined classical-bit, qubit, and e-bit space \cite{arxiv:2202.02184}.
 
 features:
-  rate: 'Tradeoff between classical communication, quantum communication, and entanglement distribution has been examined \cite{arxiv:0811.4227,arxiv:0901.3038,arxiv:0903.3920}; see also Ref. \cite{arXiv:quant-ph/0501045}.'
+  rate: 'Tradeoff between classical communication, quantum communication, and entanglement distribution has been examined \cite{arxiv:0811.4227,arxiv:0901.3038,arxiv:0903.3920}; see also Ref. \cite{arxiv:quant-ph/0501045}.'
 
 relations:
   parents:

codes/oaecc.yml

@@ -28,7 +28,7 @@ description: |-
   \begin{align}\mathcal{A} = \bigoplus_\gamma I_\gamma \otimes \mathcal{L}(\mathsf{B}_\gamma),\end{align}
   where \(\mathcal{L}(\mathsf{B}_\gamma)\) denotes the full set of linear maps on \(\mathsf{B}_\gamma\).
   The \(\mathsf{A}_j\) factors can be used to store quantum information, \(\gamma\) indexes the block structure of the code, while \(\mathsf{B}_j\) determine its gauge structure.
-  Together, the above forms the most general form of an information preserving structure \cite{arxiv:0705.4282,arxiv:1006.1358}.
+  Together, the above forms the most general form of an information preserving structure \cite{arxiv:quant-ph/0402056,arxiv:quant-ph/0507213,arxiv:0705.4282,arxiv:1006.1358}.
 
 protection: |
   Given an error operation \(\mathcal{E}\), one says that \(\mathcal{A}\) is \textit{correctable} for \(\mathcal{E}\) if there exists a recovery operation \(\mathcal{R}\) such that

codes/quantum/categories/gauge/dijkgraaf_witten.yml

@@ -8,15 +8,15 @@ physical: categories
 logical: categories
 
 name: 'Dijkgraaf-Witten gauge theory code'
-introduced: '\cite{doi:10.1007/bf02096988,arXiv:hep-th/9111004,arXiv:1212.0835}'
+introduced: '\cite{doi:10.1007/bf02096988,arxiv:hep-th/9111004,arxiv:1212.0835}'
 
 description: |
-  A code whose codewords realize \(D\)-dimensional lattice Dijkgraaf-Witten gauge theory \cite{doi:10.1007/bf02096988,arXiv:hep-th/9111004} for a finite group \(G\) and a \(D+1\)-cocycle \(\omega\) in the cohomology class \(H^{D+1}(G,U(1))\).
+  A code whose codewords realize \(D\)-dimensional lattice Dijkgraaf-Witten gauge theory \cite{doi:10.1007/bf02096988,arxiv:hep-th/9111004} for a finite group \(G\) and a \(D+1\)-cocycle \(\omega\) in the cohomology class \(H^{D+1}(G,U(1))\).
   When the cocycle is non-trivial, the gauge theory is called a \textit{twisted gauge theory}.
   For trivial cocycles in 3D, the model can be called a \textit{quantum triple model}, in allusion to being a 3D version of the quantum double model.
-  There exist lattice-model formulations in arbitrary spatial dimension \cite{arxiv:1212.0835} as well as explicitly in 3D \cite{arXiv:1404.7854,arxiv:1409.3216}.
+  There exist lattice-model formulations in arbitrary spatial dimension \cite{arxiv:1212.0835} as well as explicitly in 3D \cite{arxiv:1404.7854,arxiv:1409.3216}.
 
-  Boundaries and excitations have been studied in 3D \cite{arXiv:1807.11083,arXiv:2006.06536,arXiv:2401.13042} and arbitrary dimension \cite{arXiv:1905.08673}.
+  Boundaries and excitations have been studied in 3D \cite{arxiv:1807.11083,arxiv:2006.06536,arxiv:2401.13042} and arbitrary dimension \cite{arxiv:1905.08673}.
   Generalizations of Ocneanu's tube algebras \cite{manual:{Ocneanu, Adrian. "Chirality for operator algebras." Subfactors (Kyuzeso, 1993) 39 (1994).},doi:10.2969/aspm/03110235} can be used to characterize excitations, which are described by the tube algebra of the category \(\text{Vec}^{\omega}(G)\) for 3D models \cite{arxiv:1905.08673,arxiv:2305.17165}.
   Gapped boundaries of the 3D models are classified by a subgroup \(K \subseteq G\) and a particular three-cochain \cite{arxiv:1807.11083}.