~

codes/classical/bits/covering/nearly_perfect.yml

@@ -8,10 +8,10 @@ physical: bits
 logical: bits
 
 name: 'Nearly perfect code'
-introduced: '\cite{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}}'
+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: |
-  An \((n,K,2t+1)\) binary code is nearly perfect if parameters \(n\), \(K\), and \(t\) are such that the Johnson bound
+  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
   \end{align}

codes/classical/q-ary_digits/q-ary_digits_into_q-ary_digits.yml

@@ -85,8 +85,8 @@ protection: |
   \end{defterm}
 
   \subsection{Bounds on code parameters}
-  Bounds on the parameters of an \((n,K,d)_q\) code include the Hamming a.k.a. sphere-packing bound, Singleton bound, Gilbert-Varshamov (GV) bound, Griesmer bound, Plotkin bound, and various linear programming (LP) bounds; see \cite{preset:HKSbasics}.
-  A code whose parameters attain the Hamming bound (Singleton bound, Griesmer bound, Delsarte LP bound) is called a perfect code (an MDS code, a Griesmer code, an \hyperref[code:univ_opt_q-ary]{LP universally optimal code}).
+  Bounds on the parameters of an \((n,K,d)_q\) code include the Hamming a.k.a. sphere-packing bound, Singleton bound, Gilbert-Varshamov (GV) bound, Griesmer bound, Plotkin bound, Johnson bound, and various linear programming (LP) bounds; see \cite{preset:HKSbasics}.
+  A code whose parameters attain the Hamming bound (Singleton bound, Griesmer bound, Johnson bound, Delsarte LP bound) is called a perfect code (an MDS code, a Griesmer code, a nearly perfect code, an \hyperref[code:univ_opt_q-ary]{LP universally optimal code}).
 
   \begin{defterm}{Gilbert-Varshamov (GV) bound}
   \label{topic:gv-bound}
@@ -102,6 +102,7 @@ protection: |
   where \(h_q\) is the \(q\)-ary entropy function,
   \begin{align}
     h_{q}(\delta)=-\delta\log_{q}\frac{\delta}{q-1}-(1-\delta)\log_{q}(1-\delta)~.
+  \end{align}
   \end{defterm}
 
 features:

codes/quantum/properties/block/quantum_mds.yml

@@ -12,9 +12,7 @@ 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 is satisfied.
-
-  In other words, 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 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},
   \begin{align}
   K \leq q^{n-2(d-1)}
   \end{align}

codes/quantum/properties/block/quantum_perfect.yml

@@ -10,9 +10,7 @@ name: 'Perfect quantum code'
 #introduced: ''
 
 description: |
-  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 is satisfied,
-  
-  In other words, the quantum Hamming bound \cite{arxiv:quant-ph/9602022}
+  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
   \end{align}