subspace refs

errorcorrectionzoo · Aug 23, 2024 · e19d6a5 · e19d6a5
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diff --git a/codes/classical/matrices/rank-metric/gabidulin.yml b/codes/classical/matrices/rank-metric/gabidulin.yml
@@ -8,10 +8,12 @@ physical: matrices
 logical: matrices
 
 name: 'Gabidulin code'
-introduced: '\cite{manual:{E. M. Gabidulin, \textit{Theory of Codes with Maximum Rank Distance}, Problemy Peredachi Informacii, Volume 21, Issue 1, \emph{3–16} (1985)},doi:10.1109/18.75248}'
+introduced: '\cite{manual:{E. M. Gabidulin, \textit{Theory of Codes with Maximum Rank Distance}, Problemy Peredachi Informacii, Volume 21, Issue 1, \emph{3–16} (1985)},doi:10.1016/0097-3165(78)90015-8,doi:10.1109/18.75248}'
 
 alternative_names:
   - 'Vector rank-metric code'
+  - 'Delsarte-Gabidulin code'
+#HKS Ch 29
 
 description: |
   A linear code over \(GF(q^N)\) that corrects errors over rank metric instead of the traditional Hamming distance. Every element \(GF(q^N)\) can be written as an \(N\)-dimensional vector with coefficients in \(GF(q)\), and the rank of a set of elements is rank of the matrix formed by their coefficients.

diff --git a/codes/classical/q-ary_digits/projective/subspace.yml b/codes/classical/q-ary_digits/projective/subspace.yml
@@ -14,14 +14,25 @@ description: |
   A code that is a set of subspaces of a projective space \(PG(n-1,q)\).
 
 protection: |
-  Subspace codes are quantified with respect to the subspace distance \cite{doi:10.1109/TIT.2008.926449}; see \cite{preset:HKSnetwork}.
+  Subspace codes are quantified with respect to the subspace distance \cite{doi:10.1109/TIT.2008.926449} or injection distance \cite{arxiv:0805.3824}.'
+  
+  Generalizations of various bounds for ordinary \(q\)-ary codes have been developed for subspace codes; see \cite{preset:HKSnetwork}.
+
+features:
+  decoding:
+    - 'List decoding up to the Singleton bound \cite{doi:10.1145/2488608.2488715}.'
 
 realizations:
-  - 'Wireless networks \cite{preset:HKSnetwork}.'
+  - 'Packet-based transmission over networks \cite{preset:HKSnetwork}.'
 
 relations:
   parents:
     - code_id: projective
+  cousins:
+    - code_id: gabidulin
+      detail: 'Gabidulin codes can be used to construct asymptotically good subspace codes \cite{doi:10.1109/TIT.2003.809567,doi:10.1109/TIT.2008.926449}.'
+    - code_id: rank_metric
+      detail: 'Subspace and rank-metric codes are closely related \cite{doi:10.1109/TIT.2008.928291}.'
 
 
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