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Author: valbert4

codes/classical/bits/cyclic/quad_residue/golay.yml

@@ -13,9 +13,11 @@ 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}.
   Up to equivalence, it is unique for its 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{preset:Feit,doi:10.1016/0012-365X(74)90085-5}.
 
+  Shortening the Golay code yields \textit{shortened Golay codes} \cite{doi:10.1109/18.57203} like the \([22,10,8]\), \([22,11,7]\), and \([22,12,6]\) codes.
+  The quadruply shortened Golay code is optimal \cite{arxiv:1005.4959}.
+
   To construct the Golay code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.
   Its generator matrix is \cite[Table II]{doi:10.1109/18.720549}
   \begin{align}

codes/classical/matrices/sum-rank-metric/rank-metric/rank_metric.yml

@@ -23,6 +23,7 @@ protection: |
 
   The complexity of decoding rank-metric codes is unknown but expected to be harder than that of binary linear codes \cite{arxiv:1404.3482}.
 
+  Linear programming bounds have been derived \cite{doi:10.1016/0097-3165(78)90015-8,doi:10.1007/978-94-010-9787-1_2,doi:10.1016/j.jcta.2010.05.006}.
 
 features:
   decoders:
@@ -52,6 +53,8 @@ relations:
   parents:
     - code_id: sum_rank_metric
       detail: 'The sum-rank metric generalizes both the Hamming metric and the rank metric \cite{arxiv:1710.03109}.'
+    - code_id: 2pt_homogeneous
+      detail: 'Matrices of dimension \(m\times n\) over \(\mathbb{F}_q\) are in one-to-one correspondence with bilinear forms, which form a finite two-point homogeneous space \cite{doi:10.1016/0097-3165(78)90015-8,doi:10.1007/978-94-010-9787-1_2,doi:10.1016/j.jcta.2010.05.006}\cite[Table 2]{arxiv:1007.2905}.'
   cousins:
     - code_id: subspace
       detail: 'An \(m \times n\) rank-metric codeword \(A\) can be \textit{lifted} to a subspace codeword \((I | A)\) that generates an \(m\)-dimensional subspace \cite{arxiv:0711.0708}\cite[Def. 14.5.21]{doi:HKSprojective}.'

codes/classical/matrices/sum-rank-metric/sum_rank_metric.yml

@@ -14,6 +14,8 @@ introduced: '\cite{arxiv:1001.2059}'
 description: |
   A code whose performance is evaluated in the sum-rank metric, which is a metric that generalizes both the Hamming metric and the rank metric.
 
+protection: |
+  Linear programming bounds have been derived \cite{arxiv:2406.15926}.
 
 relations:
   parents: