berman

Author: valbert4

codes/classical/bits/reed_muller/berman.yml

@@ -0,0 +1,36 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: berman
+physical: bits
+logical: bits
+
+name: 'Berman code'
+introduced: '\cite{doi:10.1007/BF01119999,doi:10.1109/18.904535,arxiv:2202.09981}'
+
+
+description: |
+  A member of a family of codes that is recursively constructed from the single parity-check code via a construction that is similar to the \((u|u+v)\) construction \cite{arxiv:2202.09981}.
+  Berman codes include RM codes as a special case.
+
+
+features:
+  rate: 'Achieve capacity of the BEC and BMS channels \cite{arxiv:2202.09981}.'
+
+
+relations:
+  parents:
+    - code_id: binary_linear
+  cousins:
+    - code_id: uplusv
+      detail: 'Berman codes are recursively constructed via a construction that is similar to the \((u|u+v)\) construction \cite{arxiv:2202.09981}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2025-11-13'

codes/classical/bits/reed_muller/reed_muller.yml

@@ -51,6 +51,8 @@ relations:
   parents:
     - code_id: coxeter
       detail: 'An RM\((r,m)\) code is spanned by indicators of all subcubes of dimension \(m-r\) in the \(m\)-dimensional cube (this is a redundant generating set \cite{arXiv:2410.07595}), i.e., by the cosets of rank-\((m-r)\) subgroups of \(\mathbb{Z}_2^m\). For a finite Coxeter group \(W\) with \(m\) generators, the Coxeter code \(C_W(r)\) of order \(r\) with \(-1 \leq r \leq m\) is similarly spanned by indicators of all the cosets of rank-\((m-r)\) parabolic subgroups of \(W\).'
+    - code_id: berman
+      detail: 'Berman codes include RM codes as a special case \cite{arxiv:2202.09981}.'
     - code_id: uplusv
       detail: 'All RM codes can be constructed via the \((u|u+v)\) construction \cite[Ch. 13]{preset:MacSlo}.'
     - code_id: generalized_reed_muller

codes/classical/homogeneous/grassmann/grassmannian.yml

@@ -30,7 +30,7 @@ notes:
 relations:
   parents:
     - code_id: homogeneous_space_classical
-      detail: 'Homogeneous spaces \(G/H\) reduce to real Grassmannians for \(G = O(p+q)\) and \(H = O(p)\times O(q)\), to complex Grassmannians for \(G = U(p+q)\) and \(H = U(p)\times U(q)\), and to quaternionic Grassmannians for \(G = Sp(p+q)\) and \(H = Sp(p)\times Sp(q)\).'
+      detail: 'Grassmannians are symmetric spaces \(G/H\) for \(G = O(p+q)\) and \(H = O(p)\times O(q)\) in the case of real Grassmannians, \(G = U(p+q)\) and \(H = U(p)\times U(q)\) in the case of complex Grassmannians, and \(G = Sp(p+q)\) and \(H = Sp(p)\times Sp(q)\) in the case of quaternionic Grassmannians.'
   cousins:
     - code_id: t-designs
       detail: 'Designs have been formulated on Grassmannians \cite{doi:10.1023/A:1020826329555,doi:10.1016/S0012-365X(03)00151-1,arxiv:0712.1939,arxiv:1612.06729,arxiv:1705.02978}.'