~

codes/classical/bits/cyclic/binary_quad_residue.yml

@@ -16,6 +16,8 @@ description: |
 
   The roots of the generator polynomial \(r(x)\) of the first code (see \ref{topic:Cyclic-to-polynomial-correspondence}) are all of the inequivalent quadratic residues of \(n\), and the second code's generator polynomial is \((x-1)r(x)\). The roots of the generator polynomial \(a(x)\) of the third code are all inequivalent nonresidues of \(n\), and the fourth code's generator polynomial is \((x-1)a(x)\). The codes corresponding to polynomials \(r,a\) are often called \textit{augmented} quadratic-residue codes, while the remaining codes are called \textit{expurgated}.
 
+  Their automorphism group is either \(PSL(2,GF(p))\) or a closely related group by the Gleason-Prange theorem \cite{doi::10.1109/18.133245,preset:MacSlo}.
+
 features:
   decoders: 
     - 'Algebraic decoder \cite{manual:{Chen, Y. H., Truong, T. K., Chang, Y., Lee, C. D., & Chen, S. H. (2007). Algebraic decoding of quadratic residue codes using Berlekamp-Massey algorithm. Journal of information science and engineering, 23(1), 127-145.}}.'

codes/classical/bits/cyclic/golay.yml

@@ -12,7 +12,7 @@ introduced: '\cite{manual:{M. J. E. Golay, \emph{Notes on digital coding}, Proc.
 
 description: |
   A \([23, 12, 7]\) perfect binary linear code with connections to various areas of mathematics, e.g., lattices \cite{doi:10.1007/978-1-4757-6568-7} and sporadic simple groups \cite{preset:MacSlo}.
-  Adding a parity bit to the code results in the \([24, 12, 8]\) \textit{extended Golay code}.
+  Adding a parity bit to the code results in the self-dual \([24, 12, 8]\) \textit{extended Golay code}.
   Up to equivalence, both codes are unique for their respective parameters \cite{doi:10.1016/0012-365X(75)90047-3}.
   Shortening the Golay code yields the \([22,10,8]\), \([22,11,7]\), and \([22,12,6]\) \textit{shortened Golay codes} \cite{doi:10.1109/18.57203}.
   The dual of the Golay code is its \([23,11,8]\) even-weight subcode \cite{manual:{W. Feit. Some remarks on weight functions of spaces over GF(2), unpublished (1972)},doi:10.1016/0012-365X(74)90085-5}.

codes/classical/bits/easy/hamming/hamming.yml

@@ -38,6 +38,8 @@ relations:
     - code_id: q-ary_hamming
     - code_id: narrow_sense_q-ary_bch
       detail: 'Binary Hamming codes are binary primitive narrow-sense BCH codes \cite[Corr. 5.1.5]{doi:10.1017/CBO9780511807077}. Binary Hamming codes can be written in cyclic form \cite[Thm. 12.22]{preset:Hill}.'
+    - code_id: bch
+      detail: 'Binary Hamming codes are binary primitive narrow-sense BCH codes \cite[Corr. 5.1.5]{doi:10.1017/CBO9780511807077}. Binary Hamming codes can be written in cyclic form \cite[Thm. 12.22]{preset:Hill}.'
     - code_id: lexicographic
       detail: 'Hamming codes are lexicodes \cite{doi:10.1109/TIT.1986.1057187}.'
     - code_id: univ_opt_q-ary

codes/classical/q-ary_digits/ag/rm/generalized_reed_muller.yml

@@ -16,7 +16,7 @@ description: |
 
   Since \(\beta^q=\beta\) for any \(\beta\in GF(q)\), the above definition is not injective. Replacing each factor in each polynomial as \(x^q\to x\), the above set reduces to the set of all degree-\(\leq r\) polynomials in \(m\) variables such that no term has an exponent \(q\) or higher on any variable.
 
-  Its automorphism group is the general affine group \(GA(m,GF(q))\).
+  Its automorphism group is the general affine group \(GA(m,GF(q))\) \cite{doi:10.1016/0012-365X(93)90321-J}.
   Any nontrivial \(q\)-ary linear code invariant under this group is equivalent to a GRM code \cite{doi:10.1109/TIT.1970.1054554}.
 
 protection: 'Code parameters for specific \(m,r\) are given in Ref. \cite{preset:TVNAlgCodes}\cite[pg. 46]{doi:10.1007/978-94-011-3810-9}.'

codes/quantum/properties/block/topological/topological.yml

@@ -123,10 +123,11 @@ relations:
   parents:
     - code_id: block_quantum
       detail: 'Topological codes are block codes because an infinite family of tensor-product Hilbert spaces is required to formally define a phase of matter.'
-  cousins:
     - code_id: hamiltonian
       detail: 'Codespace of a topological code is typically the ground-state or low-energy subspace of a geometrically local Hamiltonian admitting a topological phase.
-      Logical qubits can also be created via lattice defects or by appropriately scheduling measurements of gauge generators (see Floquet codes).'
+      Logical qubits can also be created via lattice defects or by appropriately scheduling measurements of gauge generators (see Floquet codes).
+      Geometrically local frustration-free code Hamiltonians on Euclidean manifolds are stable with respect to small perturbations when they satisfy the local topological quantum order condition (cf. the \hyperref[topic:tqo]{TQO conditions}), meaning that a notion of a phase can be defined \cite{arxiv:1109.1588,arxiv:2110.11194}.'
+  cousins:
     - code_id: cluster_state
       detail: 'There exist necessary and sufficient conditions for a family of cluster states to exhibit the TQO-1 property \cite{arxiv:2112.02502}.'