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codes/quantum/qubits/stabilizer/stabilizer_over_gf4.yml

@@ -7,7 +7,7 @@ code_id: stabilizer_over_gf4
 physical: qubits
 logical: qubits
 
-name: 'Hermitian-construction qubit code'
+name: 'Hermitian qubit code'
 introduced: '\cite{arXiv:quant-ph/9608006}'
 
 # alternative_names:
@@ -16,7 +16,7 @@ introduced: '\cite{arXiv:quant-ph/9608006}'
 description: |
   An \([[n,k,d]]\) stabilizer code constructed from a Hermitian self-orthogonal linear quaternary code using the one-to-one correspondence between the four Pauli matrices \(\{I,X,Y,Z\}\) and the four elements \(\{0,1,\alpha^2,\alpha\}\) of the quaternary field \(GF(4)\).
 
-  Hermitian-construction codes are in one-to-one correspondence with trace-Hermitian self-orthogonal additive codes via the \hyperref[topic:gf4-representation]{\(GF(4)\) representation}.
+  Hermitian codes are in one-to-one correspondence with trace-Hermitian self-orthogonal additive codes via the \hyperref[topic:gf4-representation]{\(GF(4)\) representation}.
   Quaternary linear codes are Hermitian self-orthogonal (self-dual) iff they are trace-Hermitian self-orthogonal (self-dual) additive \cite[Thm. 27.4.1]{preset:HKSquantum} (\cite[Thm. 9.10.3]{doi:10.1017/CBO9780511807077}).
   In other words, if the underlying quaternary code is linear, then the extra trace operation can be removed from the definition of inner product.
 
@@ -32,7 +32,7 @@ relations:
     - code_id: stabilizer_over_gfqsq
   cousins:
     - code_id: dual
-      detail: 'Hermitian-construction codes are constructed from Hermitian self-orthogonal linear codes over \(GF(4)\) via the \hyperref[topic:gf4-representation]{\(GF(4)\) representation}.'
+      detail: 'Hermitian codes are constructed from Hermitian self-orthogonal linear codes over \(GF(4)\) via the \hyperref[topic:gf4-representation]{\(GF(4)\) representation}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml

@@ -7,7 +7,7 @@ code_id: stabilizer_over_gfqsq
 physical: galois
 logical: galois
 
-name: 'Hermitian-construction code'
+name: 'Hermitian code'
 introduced: '\cite{doi:10.1109/18.959288,arXiv:quant-ph/0508070}'
 
 # alternative_names:
@@ -17,7 +17,7 @@ description: |
   An \([[n,k,d]]_q\) true Galois-qudit stabilizer code constructed from a Hermitian self-orthogonal linear code over \(GF(q^2)\) using the one-to-one correspondence between the Galois-qudit Pauli matrices and elements of the Galois field \(GF(q^2)\).
 
   Galois-qudit stabilizer codes are in one-to-one correspondence with trace-alternating self-orthogonal additive codes of length \(n\) over \(GF(q^2)\) via the \hyperref[topic:gfqsq-representation]{\(GF(q^2)\) representation}.
-  Hermitian self-orthogonal linear codes over \(GF(q^2)\) are automatically trace-alternating self-orthogonal, and applying this mapping to such codes yields Hermitian-construction codes \cite[Corr. 19]{arxiv:quant-ph/0508070}.
+  Hermitian self-orthogonal linear codes over \(GF(q^2)\) are automatically trace-alternating self-orthogonal, and applying this mapping to such codes yields Hermitian codes \cite[Corr. 19]{arxiv:quant-ph/0508070}.
 
 protection: |
   A Hermitian self-orthogonal linear \([n,k,d]_{q^2}\) code yields an \([[n,n-2k]]_q\) true stabilizer code with distance no less than \(d\); this is called the \textit{Hermitian construction}.
@@ -37,10 +37,10 @@ protection: |
 relations:
   parents:
     - code_id: galois_true_stabilizer
-      detail: 'Hermitian-construction codes are true stabilizer codes because they are based on Hermitian self-orthogonal linear (as opposed to additive) codes over \(GF(q^2)\).'
+      detail: 'Hermitian codes are true stabilizer codes because they are based on Hermitian self-orthogonal linear (as opposed to additive) codes over \(GF(q^2)\).'
   cousins:
     - code_id: dual
-      detail: 'Hermitian-construction codes are constructed from Hermitian self-orthogonal linear codes over \(GF(q^2)\) via the \hyperref[topic:gfqsq-representation]{\(GF(q^2)\) representation}.'
+      detail: 'Hermitian codes are constructed from Hermitian self-orthogonal linear codes over \(GF(q^2)\) via the \hyperref[topic:gfqsq-representation]{\(GF(q^2)\) representation}.'
     - code_id: quantum_mds
       detail: 'Many MDS codes are constructed from Hermitian self-orthogonal codes over \(GF(q^2)\) using the Hermitian construction \cite{arxiv:quant-ph/0312164,arxiv:0906.2509,arxiv:1507.08355,arxiv:1803.07927}, in particular from cyclic \cite{doi:10.1109/TIT.2011.2159039}, constacyclic \cite{doi:10.1109/TIT.2014.2308180,doi:10.1109/TIT.2015.2388576} and negacyclic \cite{doi:10.1109/TIT.2012.2220519} codes.'
     - code_id: matrix_product