refs

codes/classical/analog/modulation/modulation.yml

@@ -18,7 +18,7 @@ description: |
     \textit{Quadrature amplitude modulation (QAM)} associates each pair of points with a complex-valued two-quadrature amplitude of band-limited signal \cite[Ch. 16]{doi:10.1017/9781316822708}.
 
 notes:
-  - 'See the book \cite{manual:{Proakis, John G., and Masoud Salehi. Digital communications. Vol. 4. New York: McGraw-hill, 2001.}} for an introduction to modulation schemes.'
+  - 'See books \cite{manual:{Proakis, John G., and Masoud Salehi. Digital communications. Vol. 4. New York: McGraw-hill, 2001.},doi:10.1016/B978-0-12-373580-5.X5033-9} for an introduction to modulation schemes.'
 
 relations:
   parents:

codes/classical/bits/combinatorial_design.yml

@@ -34,7 +34,7 @@ description: |
 
 
 notes:
-  - 'See \cite{doi:10.1090/surv/175,preset:HKSdesigns} for reviews on combinatorial designs.'
+  - 'See \cite{doi:10.1090/surv/175,preset:HKSdesigns,arxiv:0811.1254} for reviews on combinatorial designs.'
   - 'See \cite{doi:10.1017/CBO9780511549533,doi:10.1201/9781420010541,doi:10.1017/CBO9780511623714,doi:10.1007/b97564} for books on combinatorial designs.'
 
 relations:

codes/classical/bits/tanner/qc/difference_set.yml

@@ -17,14 +17,22 @@ description: |
   Certain DCS codes satisfy more redundant constraints than Gallager codes and thus can outperform them \cite{doi:10.1007/978-1-4613-0165-3_6}.
 
 notes:
-  - 'See book \cite{doi:10.1142/9283} for a general theory of linear codes made from difference sets.'
+  - 'See book \cite[Ch. 6]{doi:10.1142/9283} for a general theory of linear codes made from difference sets.'
 
 
 relations:
   parents:
     - code_id: qc_ldpc
     - code_id: algebraic_ldpc
-    - code_id: cyclic
+    - code_id: binary_cyclic
+  cousins:
+    - code_id: hadamard
+      detail: '\textit{Hadamard difference sets} are difference sets constructed from Hadamard matrices \cite[Ch. 6]{doi:10.1142/9283}.'
+    - code_id: hyperoval
+      detail: 'Hyperoval difference sets yield DSC codes \cite{doi:10.1023/A:1008264606494}\cite[Ch. 6]{doi:10.1142/9283}.'
+    - code_id: generalized_reed_muller
+      detail: 'DSC codes can be \hyperref[topic:finite-fields]{subfield} subcodes of GRM codes, and visa versa \cite[Thm. 6.14]{doi:10.1142/9283}.'
+
 
 
 # Begin Entry Meta Information

codes/classical/bits/tanner/regular_tanner/regular_binary_tanner.yml

@@ -41,6 +41,8 @@ features:
 
   decoders:
     - 'Parallel decoding algorithm corrects a fraction \(\delta_0^2/48\) of errors for Tanner codes \cite{doi:10.1109/18.556667}. A modification of said algorithm improves the fraction to \(\delta_0^2/4\) with no extra cost to complexity \cite{doi:10.1109/18.910593}.'
+    - 'Soft-decision linear-time decoder correcting errors almost up to half of the Blokh-Zyablov bound \cite{doi:10.1109/TIT.2005.846392}.'
+
 
 realizations:
   - 'First hardware implementation was done using a semi-systolic decoding architecture \cite{doi:10.1016/0166-218X(91)90111-9}.'

codes/classical/matrices/raid/x_array.yml

@@ -12,12 +12,13 @@ name: 'X-code'
 introduced: '\cite{doi:10.1109/18.746809}'
 
 description: |
-  Array code with a simple geometrical construction that achieves optimal encoding and update complexity.
+  An MDS array code with a simple geometrical construction that achieves optimal encoding and update complexity.
 
 
 relations:
   parents:
     - code_id: array
+    - code_id: mds
 
 
 # Begin Entry Meta Information

codes/classical/q-ary_digits/ag/evaluation_varieties.yml

@@ -28,6 +28,7 @@ description: |
   Forms are the most general cases considered for evaluation codes since they encompass all polynomials via the reverse of the above procedure.
 
   One can specify the space \(L\) by the number of variables input into the rational functions as well as their maximum degree. One can additionally select only functions that have zeroes at certain points with certain multiplicities. A bookkeeping device for this data is the \textit{divisor} \(D\), and the corresponding vector space of functions defined using the variety \(\cal X\) and the divisor is the \textit{Riemann-Roch space} \(L=L(D)\) \cite[pg. 313]{preset:HKSag}.
+  Codes based on divisors with only one pole (of arbitrary order) are called \textit{one-point codes} \cite[Remark 4.4]{preset:HPAlgCodes}.
 
 
 protection: 'Properties of the underlying geometric object \(\cal X\) can be used to bound the code dimension \(k\) and distance \(d\). The order or Feng-Rao bound gives a lower bound on the distance of evaluation codes \cite{doi:10.1142/9789812794017_0004,doi:10.1109/18.179340,preset:HPAlgCodes}; see \cite[Ch. 4]{preset:HPAlgCodes}\cite{arxiv:0802.2349} for more discussion.'

codes/quantum/qubits/stabilizer/qldpc/homological/qubit_generalized_homological_product.yml

@@ -15,7 +15,7 @@ relations:
     - code_id: qubit_css
     - code_id: generalized_homological_product_css
   cousins:
-    - code_id: cyclic
+    - code_id: binary_cyclic
       detail: 'Iterative tensor-product codes can be constructed out of CSS codes that in turn stem from cyclic codes \cite{arxiv:1512.07081}.'
     - code_id: quantum_reed_muller
       detail: 'Iterative tensor-product codes can be constructed out of quantum Reed-Muller codes \cite{arxiv:1512.07081}.'

codes/quantum/qubits/stabilizer/topological/surface/higher_d/4d_surface.yml

@@ -45,13 +45,19 @@ features:
     - '\(1.59\%\) for independent \(X,Z\) noise and faulty syndrome measurements using the Hastings decoder \cite{arxiv:1609.00510}.'
 
 
+realizations:
+  - 'Trapped ions: single-shot QEC realized using the \([[33,1,4]]\) loop toric code on the Quantinuum H2 device \cite{arxiv:2408.08865}.'
+
+
 relations:
   parents:
     - code_id: higher_dimensional_surface
       detail: 'The 4D loop toric code realizes 4D \(\mathbb{Z}_2\) gauge theory with only loop excitations \cite{arxiv:2112.02137}.'
     - code_id: translationally_invariant_stabilizer
     - code_id: self_correct
       detail: 'The 4D loop toric code is a self-correcting quantum memory \cite{arxiv:quant-ph/0110143,arxiv:0811.0033}.'
+    - code_id: single_shot
+      detail: 'Single-shot QEC has been realized using the \([[33,1,4]]\) loop toric code on the Quantinuum H2 device \cite{arxiv:2408.08865}.'
     - code_id: topological_abelian
       detail: 'The 4D loop toric code realizes 4D \(\mathbb{Z}_2\) gauge theory with only loop excitations \cite{arxiv:2112.02137}.'