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codes/quantum/properties/block/quantum_mds.yml

@@ -14,7 +14,7 @@ introduced: '\cite{arxiv:quant-ph/9604034,arxiv:quant-ph/9702031,arxiv:quant-ph/
 description: |
   A type of block quantum code whose parameters satisfy the quantum Singleton bound with equality.
 
-  An \(((n,K,d))\) code constructed out of \(q\)-dimensional qudits is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the quantum Singleton bound \cite{arxiv:quant-ph/9604034,arxiv:quant-ph/9702031,arxiv:quant-ph/9703048},
+  An \(((n,K,d))\) code constructed out of \(q\)-dimensional qudits is a quantum MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the quantum Singleton bound \cite{arxiv:quant-ph/9604034,arxiv:quant-ph/9702031,arxiv:quant-ph/9703048},
   \begin{align}
   K \leq q^{n-2(d-1)}
   \end{align}
@@ -46,13 +46,13 @@ relations:
     - code_id: q-ary_cyclic
       detail: 'Quantum MDS codes can be constructed from \(q\)-ary cyclic codes using the Hermitian construction \cite{doi:10.1109/TIT.2011.2159039}.'
     - code_id: stabilizer_over_gfqsq
-      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,arxiv:1803.07927} and negacyclic \cite{doi:10.1109/TIT.2012.2220519} codes.'
+      detail: 'Many quantum 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,arxiv:1803.07927} and negacyclic \cite{doi:10.1109/TIT.2012.2220519} codes.'
     - code_id: constacyclic
-      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,arxiv:1803.07927}, and negacyclic \cite{doi:10.1109/TIT.2012.2220519} codes.'
+      detail: 'Many quantum 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,arxiv:1803.07927}, and negacyclic \cite{doi:10.1109/TIT.2012.2220519} codes.'
     - code_id: generalized_reed_solomon
-      detail: 'Some MDS codes are constructed from cyclic and constacyclic codes \cite{arxiv:1502.05267} which are GRS codes \cite{doi:10.1007/s10623-022-01174-5,doi:10.1007/s10623-023-01294-6}.'
+      detail: 'Some quantum MDS codes are constructed from cyclic and constacyclic codes \cite{arxiv:1502.05267} which are GRS codes \cite{doi:10.1007/s10623-022-01174-5,doi:10.1007/s10623-023-01294-6}.'
     - code_id: skew-cyclic_galois_css
-      detail: 'Some MDS codes are constructed from cyclic and constacyclic codes using the Galois-qudit CSS construction \cite{doi:10.1016/j.disc.2020.112189}.'
+      detail: 'Some quantum MDS codes are constructed from cyclic and constacyclic codes using the Galois-qudit CSS construction \cite{doi:10.1016/j.disc.2020.112189}.'
 
 
 # - code_id: cyclic