Gottesman refs

errorcorrectionzoo · Jan 26, 2025 · dfcab5e · dfcab5e
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diff --git a/codes/classical/q-ary_digits/convolutional/convolutional.yml b/codes/classical/q-ary_digits/convolutional/convolutional.yml
@@ -40,7 +40,7 @@ relations:
       detail: 'Convolutional codes for finite block size are \(q\)-ary codes.'
     - code_id: quantum_convolutional
     - code_id: reed_solomon
-      detail: 'Convolutional codes are often used in concatenation with RS codes for communication \cite{doi:10.1002/0470866969}.'
+      detail: 'Convolutional codes can be constructed from \cite{manual:{Piret, Philippe. Convolutional codes: an algebraic approach. MIT press, 1988.}} and concatenated with \cite{doi:10.1002/0470866969} RS codes.'
 
 
 # Begin Entry Meta Information

diff --git a/codes/quantum/properties/group_rep/knill.yml b/codes/quantum/properties/group_rep/knill.yml
@@ -29,6 +29,7 @@ description: |
   \end{defterm}
 
   The first example of an error basis based on a non-Abelian error group is due to S. Egner and consists of products of \(S\), Pauli, and Hadamard gates \cite{arxiv:quant-ph/9608049}.
+  Certain nice error bases have been classified and are related to the braid group \cite{arxiv:0902.0383}.
 
 notes:
   - 'Catalogue of \hyperref[topic:nice-error-basis]{nice error bases}, managed by A. Klappenecker and M. Rotteler, is available on \href{https://people.engr.tamu.edu/andreas-klappenecker/ueb/ueb.html}{this website}.'

diff --git a/codes/quantum/qubits/stabilizer/convolutional/quantum_convolutional.yml b/codes/quantum/qubits/stabilizer/convolutional/quantum_convolutional.yml
@@ -41,6 +41,10 @@ relations:
         Any prime-qudit code can be converted using a constant-depth Clifford circuit to several copies of the 1D repetition code along with some trivial codes \cite{arxiv:1607.01387}.
     - code_id: quantum_lego
       detail: 'Quantum convolutional encoding circuits can be viewed as matrix-product-state tensor networks \cite{arxiv:1312.4578}.'
+    - code_id: generalized_reed_solomon
+      detail: 'GRS codes can be used to construct quantum convolutional codes \cite{arxiv:0812.5104}.'
+    - code_id: generalized_reed_muller
+      detail: 'GRM codes can be used to construct quantum convolutional codes \cite{arxiv:quant-ph/0604102,arxiv:0812.5104,doi:10.1201/9781584889007-18}.'
 
 
 # Begin Entry Meta Information

diff --git a/codes/quantum/qubits/stabilizer/qldpc/pg_qldpc.yml b/codes/quantum/qubits/stabilizer/qldpc/pg_qldpc.yml
@@ -9,7 +9,7 @@ logical: qubits
 
 name: 'Finite-geometry (FG) QLDPC code'
 short_name: 'FG-QLDPC'
-introduced: '\cite{arxiv:0712.4115,arxiv:1207.0732,arxiv:1512.07081}'
+introduced: '\cite{arxiv:0712.4115,arxiv:0812.5104,arxiv:1207.0732,arxiv:1512.07081}'
 
 description: |
   CSS code constructed from linear binary codes whose parity-check or generator matrices are incidence matrices of points, hyperplanes, or other structures in finite geometries.

diff --git a/codes/quantum/qudits_galois/stabilizer/bch/galois_bch.yml b/codes/quantum/qudits_galois/stabilizer/bch/galois_bch.yml
@@ -9,7 +9,7 @@ logical: galois
 
 name: 'Galois-qudit BCH code'
 short_name: 'Galois-qudit BCH'
-introduced: '\cite{arxiv:quant-ph/0501126,arxiv:quant-ph/0604102,doi:10.1007/11750321_63,doi:10.1109/TIT.2006.890730,doi:10.26421/QIC13.1-2-3,doi:10.1103/PhysRevA.80.042331,arxiv:1705.00239,arxiv:2007.13309}'
+introduced: '\cite{arxiv:quant-ph/0501126,arxiv:quant-ph/0604102,doi:10.1007/11750321_63,doi:10.1109/TIT.2006.890730,arxiv:0812.5104,doi:10.26421/QIC13.1-2-3,doi:10.1103/PhysRevA.80.042331,arxiv:1705.00239,arxiv:2007.13309}'
 
 description: |
   True Galois-qudit stabilizer code constructed from BCH codes via either the Hermitian construction or the Galois-qudit CSS construction.
@@ -30,7 +30,7 @@ relations:
     - code_id: stabilizer_over_gfqsq
       detail: 'Galois-qudit BCH codes can be constructed via the CSS construction or the Hermitian construction.'
     - code_id: galois_subsystem_stabilizer
-      detail: 'Asymmetric quantum BCH codes have been constructed \cite[Lemma 4.4]{doi:10.1098/rspa.2008.0439}\cite{arxiv:quant-ph/0606107,doi:10.1109/ICCES.2008.4772987,doi:10.26421/QIC11.3-4-4}, including subsystem BCH codes \cite{arxiv:0803.0764}.'
+      detail: 'Asymmetric quantum BCH codes have been constructed \cite[Lemma 4.4]{doi:10.1098/rspa.2008.0439}\cite{arxiv:quant-ph/0606107,doi:10.1109/ICCES.2008.4772987,doi:10.26421/QIC11.3-4-4}, including subsystem BCH codes \cite{arxiv:0803.0764,arxiv:0812.5104}.'
     - code_id: qldpc
       detail: 'Some Galois-qudit BCH codes can be constructed as QLDPC codes \cite{arxiv:0802.4079}.'
 

diff --git a/codes/quantum/qudits_galois/stabilizer/duadic/galois_duadic.yml b/codes/quantum/qudits_galois/stabilizer/duadic/galois_duadic.yml
@@ -9,7 +9,7 @@ physical: galois
 logical: galois
 
 name: 'Quantum duadic code'
-introduced: '\cite{arxiv:quant-ph/0601117,arxiv:0711.2050,doi:10.1142/S0219749909004979,arxiv:2211.00891}'
+introduced: '\cite{arxiv:quant-ph/0601117,arxiv:0711.2050,arxiv:0812.5104,doi:10.1142/S0219749909004979,arxiv:2211.00891}'
 
 description: |
   True Galois-qudit stabilizer code constructed from \(q\)-ary duadic codes via the Hermitian construction or the Galois-qudit CSS construction.

diff --git a/codes/quantum/qudits_galois/stabilizer/evaluation/galois_reed_muller.yml b/codes/quantum/qudits_galois/stabilizer/evaluation/galois_reed_muller.yml
@@ -42,9 +42,11 @@ relations:
       detail: 'Galois-qudit RM codes can be constructed via the CSS construction or the Hermitian construction.'
   cousins:
     - code_id: generalized_reed_muller
+      detail: 'Generalized RM codes can be used to construct Galois-qudit RM codes.'
+    - code_id: projective_reed_muller
+      detail: 'Projective RM codes can be used to construct Galois-qudit RM codes \cite{doi:10.1201/9781584889007-18,arxiv:0812.5104}.'
     - code_id: quantum_mds
-      detail: 'There exists a quantum RM code \([[q, q − 2ν − 2, ν + 2]]_q\) for \( 0\leq v \leq \frac{(q-2)}{2}\) and \([[q^2,q^2-2v-2,v+2]]_q\) for
-      \(0\leq v \leq q-2\). Both these codes satisfy the quantum Singleton bound.'
+      detail: 'There exists a quantum RM code \([[q, q − 2ν − 2, ν + 2]]_q\) for \( 0\leq v \leq \frac{(q-2)}{2}\) and \([[q^2,q^2-2v-2,v+2]]_q\) for \(0\leq v \leq q-2\). Both these codes satisfy the quantum Singleton bound.'
     - code_id: galois_css
       detail: 'Galois-qudit RM codes can be constructed via the CSS construction or the Hermitian construction.'
     - code_id: stabilizer_over_gfqsq