fixes

codes/quantum/qubits/stabilizer/qldpc/homological/balanced_product/hypergraph_product.yml

@@ -19,7 +19,7 @@ description: |
   A member of a family of CSS codes whose stabilizer generator matrix is obtained from a hypergraph product of two classical linear binary codes.
   Codes from hypergraph products in higher dimension are called \textit{higher-dimensional HGP codes} \cite{arxiv:1810.01519}.
 
-  More technically, the \(x\)- and \(Z\)-type stabilizer generator matrices of a hypergraph product code are, respectively, the boundary and coboundary operators of the 2-complex obtained from the tensor product of a chain complex and cochain complex corresponding to two classical linear binary \textit{seed} codes.
+  More technically, the \(X\)- and \(Z\)-type stabilizer generator matrices of a hypergraph product code are, respectively, the boundary and coboundary operators of the 2-complex obtained from the tensor product of a chain complex and cochain complex corresponding to two classical linear binary \textit{seed} codes.
   Let the two seed codes be \(C_i\) for \(i\in\{1,2\}\) with parameters \([n_i, k_i, d_i]\), defined as the kernel of \(r_i \times n_i\) check matrices \(H_i\) of rank \(n_i - k_i\).
   The hypergraph product yields two classical codes \(C_{X,Z}\) with parity-check matrices
   \begin{align}

codes/quantum/qudits_galois/stabilizer/css/two_block_quantum.yml

@@ -15,7 +15,8 @@ alternative_names:
   - 'Two-square-block code'
 
 description: |
-  Galois-qudit CSS code whose stabilizer generator matrices \(H_X=(A,B)\) and \(H_Z=(B^T,-A^T)\), are constructed from a pair of square commuting matrices \(A\) and \(B\).
+  Galois-qudit CSS code whose stabilizer generator matrices \(H_X=(A_1,B_1)\) and \(H_Z=(B^T_2,-A^T_2)\), are constructed from four matrices satisfying \(A_1 B_2 - B_1 A_2 = 0\).
+  In the case the two pairs are equal, we have \(H_X=(A,B)\) and \(H_Z=(B^T,-A^T)\), constructed from a pair of square commuting matrices \(A\) and \(B\).
 
   Generalized constructions utilizing more than two blocks have also been considered \cite{arxiv:2310.15092}.
 

codes/quantum/qudits_galois/stabilizer/qldpc/balanced_product/lp/scalar/2bga.yml

@@ -44,7 +44,7 @@ description: |
   \end{align} and the
   binary algebra \(\mathbb{F}_2[T]\).  Select \(a=1+x+y+x^{-1}yx\)
   and \(b=1+x+y+yx\) to get an \emph{essentially non-Abelian} 2BGA code
-  LP\([a,b]\) with parameters \([[24,5,3]]_2\) \cite{arxiv:2306.16400}.
+  LP\([a,b]\) with parameters \([[24,5,3]]\) \cite{arxiv:2306.16400}.
 
 # \subsection{Examples}
 #
@@ -111,11 +111,11 @@ features:
     \(W\le 8\), block lengths \(n\le 100\), and parameters such that
     \(kd\ge n\) have been constructed by
     exhaustive enumeration \cite{arxiv:2306.16400}.  Examples include GB codes with parameters
-    \([[70,8,10]]_2\), \([[72,10,9]]_2\), Abelian 2BGA for groups
+    \([[70,8,10]]\), \([[72,10,9]]\), Abelian 2BGA for groups
     \(\mathbb{Z}_{mh}=\mathbb{Z}_m\times \mathbb{Z}_2\) (index-4 QC codes) with parameters
-    \([[48,8,6]]_2\) and \([[56,8,7]]_2\), and non-Abelian codes with
-    parameters \([[64,8,8]]_2\), \([[82,10,9]]_2\), \([[96,10,12]]_2\),
-    and \([[96,12,10]]_2\) (all of these have stabilizer generators of
+    \([[48,8,6]]\) and \([[56,8,7]]\), and non-Abelian codes with
+    parameters \([[64,8,8]]\), \([[82,10,9]]\), \([[96,10,12]]\),
+    and \([[96,12,10]]\) (all of these have stabilizer generators of
     weight \(W=8\).)