norm_trace

codes/classical/q-ary_digits/ag/evaluationAG/hermitian.yml

@@ -56,8 +56,8 @@ features:
 
 relations:
   parents:
-    - code_id: evaluation
-      detail: 'Hermitian codes are evaluation AG codes with \(\cal X\) being a Hermitian curve \cite{doi:10.1017/CBO9780511543401}\cite[Ex. 2.74]{preset:HPAlgCodes}. This curve is maximal, meaning that Hermitian codes are evaluation AG codes with maximum possible length given a fixed genus.'
+    - code_id: norm_trace
+      detail: 'Hermitian codes are evaluation AG codes with \(\cal X\) being a Hermitian curve \cite{doi:10.1017/CBO9780511543401}\cite[Ex. 2.74]{preset:HPAlgCodes}. This curve is maximal, meaning that Hermitian codes are evaluation AG codes with maximum possible length given a fixed genus. They are a special case of norm-trace codes \cite{doi:10.1016/S1071-5797(03)00010-8}.'
   cousins:
     - code_id: generalized_reed_solomon
       detail: 'Hermitian codes are concatenated GRS codes \cite{doi:10.1007/BF00124208}.'

codes/classical/q-ary_digits/ag/evaluationAG/norm_trace.yml

@@ -0,0 +1,34 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: norm_trace
+physical: q-ary_digits
+logical: q-ary_digits
+
+name: 'Norm-trace code'
+introduced: '\cite{doi:10.1016/S1071-5797(03)00010-8}'
+
+
+description: |
+  Evaluation AG code of rational functions evaluated on points lying on a Miura-Kamiya curve in either affine or projective space.
+  The family is named as such because the equations defining the curves can be expressed in terms of the \hyperref[topic:finite-fields]{norm and trace of a field extension}.
+
+
+protection: |
+  Minimum distance is determined by an order bound \cite{doi:10.1016/S1071-5797(03)00010-8}.
+
+
+relations:
+  parents:
+    - code_id: evaluation
+      detail: 'Norm-trace codes are evaluation AG codes with \(\cal X\) being a Miura-Kamiya curve \cite{doi:10.1016/S1071-5797(03)00010-8}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-08-17'

codes/quantum/qubits/qubits_into_qubits.yml

@@ -115,7 +115,7 @@ features:
       \begin{align}
         C_k = \{ U | U P U^{\dagger} \in C_{k-1} \}~,
       \end{align}
-      where \(P\) is any Pauli matrix, and \(C_1\) is the \hyperref[topic:pauli]{Pauli group}.
+      where \(P\) is any Pauli matrix, where \(C_1\) is the \hyperref[topic:pauli]{Pauli group}, and where \(C_2\) is the \hyperref[topic:clifford]{Clifford group}.
       \end{defterm}'
     - 'Arbitrary \(n\)-qubit circuits can be implemented fault-tolerantly in a 3D architecture using \(O(n^{3/2}\log^3 n)\) qubits, and in a 2D architecture using only \(O(n^2 \log^3 n)\) qubits \cite{arxiv:2402.13863}.'
   decoders: