~

codes/classical/bits/covering/nearly_perfect.yml

@@ -11,6 +11,8 @@ name: 'Nearly perfect code'
 introduced: '\cite{doi:10.1109/TIT.1962.1057714,doi:10.1016/0012-365X(72)90025-8,manual:{N. V. Semakov, V. A. Zinov''ev, G. V. Zaitsev, “Uniformly Packed Codes”, Probl. Peredachi Inf., 7:1 (1971), 38–50; Problems Inform. Transmission, 7:1 (1971), 30–39}}'
 
 description: |
+  A type of binary code whose parameters satisfy the Johnson bound with equality.
+
   An \((n,K,2t+1)\) binary code is nearly perfect if parameters \(n\), \(K\), and \(t\) are such that the Johnson bound \cite{doi:10.1109/TIT.1962.1057714},
   \begin{align}
     \frac{{n \choose t}\left(\frac{n-t}{t+1}-\left\lfloor \frac{n-t}{t+1}\right\rfloor \right)}{\left\lfloor \frac{n}{t+1}\right\rfloor }+\sum_{j=0}^{t}{n \choose j}\leq2^{n}/K

codes/classical/q-ary_digits/covering/perfect.yml

@@ -10,6 +10,8 @@ logical: q-ary_digits
 name: 'Perfect code'
 
 description: |
+  A type of \(q\)-ary code whose parameters satisfy the Hamming bound with equality.
+
   An \((n,K,2t+1)_q\) code is perfect if parameters \(n\), \(K\), \(t\), and \(q\) are such that the Hamming (a.k.a. sphere-packing) bound
   \begin{align}
   \sum_{j=0}^{t}(q-1)^{j}{n \choose j}\leq q^{n}/K

codes/classical/q-ary_digits/distributed_storage/mds.yml

@@ -12,7 +12,9 @@ short_name: 'MDS'
 introduced: '\cite{doi:10.1109/TIT.1964.1053661}'
 
 description: |
-  A \([n,k,d]_q\) binary or \(q\)-ary linear code is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the Singleton bound
+  A type of \(q\)-ary code whose parameters satisfy the Singleton bound with equality.
+
+  A \([n,k,d]_q\) \(q\)-ary linear code is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the Singleton bound
   \begin{align}
   d \leq n-k+1
   \end{align}

codes/classical/q-ary_digits/projective/griesmer.yml

@@ -13,6 +13,8 @@ introduced: '\cite{doi:10.1147/rd.45.0532,doi:10.1016/S0019-9958(65)90080-X,manu
 # Varshamov ref from footnote in http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ppi&paperid=1040&option_lang=eng
 
 description: |
+  A type of \(q\)-ary code whose parameters satisfy the Griesmer bound with equality.
+
   A \([n,k,d]_q\) code is a Griesmer code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the Griesmer bound
   \begin{align}
     n\geq\sum_{j=0}^{k-1}\left\lceil \frac{d}{q^{j}}\right\rceil ~,

codes/quantum/properties/block/quantum_mds.yml

@@ -12,7 +12,9 @@ short_name: 'Quantum MDS'
 introduced: '\cite{arxiv:quant-ph/9604034,arxiv:quant-ph/9702031,arxiv:quant-ph/9703048}'
 
 description: |
-  An \(((n,K,d))\) code constructed out of \(q\)-dimensional qubits or Galois 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},
+  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},
   \begin{align}
   K \leq q^{n-2(d-1)}
   \end{align}

codes/quantum/properties/block/quantum_perfect.yml

@@ -10,6 +10,8 @@ name: 'Perfect quantum code'
 #introduced: ''
 
 description: |
+  A type of block quantum code whose parameters satisfy the quantum Hamming bound with equality.
+
   A \hyperref[topic:degeneracy]{non-degenerate} code constructed out of \(q\)-dimensional qudits and having parameters \(((n,K,2t+1))\) is perfect if \(n\), \(K\), \(t\), and \(q\) are such that the quantum Hamming bound \cite{arxiv:quant-ph/9602022},
   \begin{align}
   \sum_{j=0}^{t}(q^2-1)^{j}{n \choose j}\leq q^{n}/K