dual_over_z4, self_dual_over_z4

Author: valbert4

codelists/descendants/classical/list_self_dual.yml

@@ -7,11 +7,15 @@ intro: |
 codes:
   select:
     - descendant_of: self_dual_over_rings
+    - descendant_of: self_dual_additive
     - descendant_of: self_dual_polytope
     - descendant_of: self_dual_lattice
     - cousin_of: self_dual_over_rings
-    - cousin_of: self_dual_over_zq
     - cousin_of: self_dual_additive
+    - cousin_of: self_dual_polytope
+    - cousin_of: self_dual_lattice
+    - cousin_of: self_dual_over_zq
+    - cousin_of: self_dual_over_z4
     - cousin_of: self_dual
 
 

codes/classical/analog/sphere_packing/lattice/dual/leech.yml

@@ -45,7 +45,7 @@ relations:
       detail: 'Codewords of the Leech lattice have been proposed to be used for a modulation scheme \cite{doi:10.1109/49.29618}.'
     - code_id: pseudo_golay
       detail: 'The Leech lattice can be constructed from pseudo Golay codes via \term{Construction \(A_4\)} \cite{doi:10.1016/S0012-365X(98)00358-6,arxiv:2309.02382}.'
-    - code_id: self_dual_over_zq
+    - code_id: self_dual_over_z4
       detail: 'Each 4-frame of the Leech lattice corresponds to an extremal Type II self-dual code over \(\mathbb{Z}_4\) \cite{doi:10.1007/s10623-023-01293-7}.'
 
 

codes/classical/rings/dual/dual_over_rings.yml

@@ -27,8 +27,6 @@ description: |
 relations:
   parents:
     - code_id: rings_linear
-  cousins:
-    - code_id: dual
 
 
 # Begin Entry Meta Information

codes/classical/rings/over_zq/dual/dual_over_zq.yml

@@ -17,10 +17,6 @@ description: |
     C^\perp = \{ y\in (\mathbb{Z}_q)^{n} ~|~ x \cdot y=0 \mod q \forall x\in C\}~.
   \end{align}
 
-protection: |
-  For \(q=4\), the dual of a code \(C=(n,4^{k_1} 2^{k_2})_{\mathbb{Z}_4}\) is \(C^{\perp} = (n,4^{n-k_1-k_2} 2^{k_2})\), whose generator matrix can be written in terms of the standard form of \(C\) \cite[Prop. 1.2]{doi:10.1142/3603}.
-
-
 
 relations:
   parents:

codes/classical/rings/over_zq/dual/self_dual_over_zq.yml

@@ -12,11 +12,6 @@ name: 'Self-dual code over \(\mathbb{Z}_q\)'
 description: |
   An additive linear code \(C\) over \(\mathbb{Z}_q\) that is equal to its dual, \(C^\perp = C\), where the dual is defined with respect to the standard inner product.
 
-  Self-dual codes for \(q=4\) contain \(2^n\) codewords \cite[Corr. 1.3]{doi:10.1142/3603}.
-
-protection: |
-  Extremal Type-II self-dual codes over \(\mathbb{Z}_4\) have been classified for \(n\leq 16\) \cite{doi:10.1109/18.651058,doi:10.1006/jcta.1996.2750}, and there are 4744 such codes at \(n=24\) \cite{doi:10.1007/s10623-023-01293-7}.
-
 notes:
   - 'See books \cite{doi:10.1007/3-540-30731-1} for more on self-dual codes over \(\mathbb{Z}_q\).'
   - 'See \href{https://www.math.is.tohoku.ac.jp/~munemasa/selfdualcodes.htm}{Database of self-dual codes} by M. Harada and A. Munemasa for a database of self-dual codes over \(\mathbb{Z}_{4}\), \(\mathbb{Z}_{6}\), \(\mathbb{Z}_{8}\), \(\mathbb{Z}_{9}\), and \(\mathbb{Z}_{10}\).'

codes/classical/rings/over_zq/over_z4/linear_over_z4/dual_over_z4.yml

@@ -0,0 +1,31 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: dual_over_z4
+physical: rings
+logical: rings
+
+name: 'Dual code over \(\mathbb{Z}_4\)'
+
+description: |
+  For any linear code \(C\) over \(\mathbb{Z}_4\), the dual code is the set of quaternary strings that are orthogonal to the codewords of \(C\) under the standard inner product modulo \(4\).
+
+protection: |
+  The dual of a code \(C=(n,4^{k_1} 2^{k_2})_{\mathbb{Z}_4}\) is \(C^{\perp} = (n,4^{n-k_1-k_2} 2^{k_2})\), whose generator matrix can be written in terms of the standard form of \(C\) \cite[Prop. 1.2]{doi:10.1142/3603}.
+
+
+
+relations:
+  parents:
+    - code_id: quaternary_over_z4
+    - code_id: dual_over_zq
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2026-01-02'

codes/classical/rings/over_zq/over_z4/linear_over_z4/rm/cmr.yml

@@ -17,8 +17,7 @@ description: |
 
 relations:
   parents:
-    - code_id: quaternary_over_z4
-    - code_id: self_dual_over_zq
+    - code_id: self_dual_over_z4
       detail: 'The \(C_{m,r}\) code is a Type IV self-dual code over \(\mathbb{Z}_4\) \cite{doi:10.1109/18.796375}.'
   cousins:
     - code_id: reed_muller

codes/classical/rings/over_zq/over_z4/linear_over_z4/rm/quaternary_reed_muller.yml

@@ -26,7 +26,7 @@ relations:
       detail: 'The mod-two reduction of the QRM\((r,m)\) code is the RM\((r,m)\) code \cite[Thm. 19]{arxiv:math/0207208}.'
     - code_id: gray
       detail: 'The mod-two reduction of the QRM\((r,m)\) code is the RM\((r,m)\) code \cite[Thm. 19]{arxiv:math/0207208}.'
-    - code_id: self_dual_over_zq
+    - code_id: dual_over_z4
       detail: 'The dual of a QRM\((r,m)\) code is the QRM\((m-r-1,m)\) code \cite[Thm. 19]{arxiv:math/0207208}.'
 
 

codes/classical/rings/over_zq/over_z4/linear_over_z4/self_dual/harada_kitazume.yml

@@ -17,8 +17,7 @@ description: |
 
 relations:
   parents:
-    - code_id: quaternary_over_z4
-    - code_id: self_dual_over_zq
+    - code_id: self_dual_over_z4
       detail: 'Harada-Kitazume codes are extremal Type II self-dual codes over \(\mathbb{Z}_4\) \cite{doi:10.1006/eujc.1999.0360}.'
   cousins:
     - code_id: niemeier

codes/classical/rings/over_zq/over_z4/linear_over_z4/self_dual/klemm.yml

@@ -27,8 +27,7 @@ description: |
 
 relations:
   parents:
-    - code_id: quaternary_over_z4
-    - code_id: self_dual_over_zq
+    - code_id: self_dual_over_z4
       detail: 'The Klemm code is a Type IV self-dual code over \(\mathbb{Z}_4\) \cite{doi:10.1109/18.796375}.'
   cousins:
     - code_id: hamming844