graph edits

valbert4 · valbert4 · commit c2a4bea8675e · 2025-11-15T13:48:14.000-05:00
diff --git a/codes/classical/groups/permutation/binary_permutation.yml b/codes/classical/groups/permutation/binary_permutation.yml
@@ -7,7 +7,7 @@ code_id: binary_permutation
 physical: groups
 
 name: 'Code in permutations'
-introduced: '\cite{doi:10.1109/PROC.1965.3680,doi:10.1109/TIT.1969.1054291,doi:10.1016/S0019-9958(79)90076-7}'
+introduced: '\cite{doi:10.1109/PROC.1965.3680,doi:10.1109/TIT.1969.1054291,doi:10.1016/0378-3758(78)90008-3,doi:10.1016/0097-3165(77)90009-7,doi:10.1016/S0019-9958(79)90076-7}'
 
 alternative_names:
   - 'Permutation-based code'
@@ -20,21 +20,26 @@ description: |
 protection: |
   Protects against errors in the Kendall tau distance on the space of permutations.
   The Kendall distance between permutations \(\sigma\) and \(\pi\) is defined as the minimum number of adjacent transpositions required to change \(\sigma\) into \(\pi\).
-  Various bounds have been developed \cite{doi:10.1016/0097-3165(79)90012-8,arxiv:0908.4094}, including LP bounds \cite{doi:10.1006/eujc.1998.0272}.
+  Various bounds have been developed \cite{doi:10.1016/0097-3165(79)90012-8,arxiv:0908.4094}, including LP bounds \cite{doi:10.1006/eujc.1998.0272,arxiv:1912.04500}.
   The mapping to inversion vectors is not distance preserving, but the \(\ell_1\) distance between inversion vectors is a lower bound on the Kendall tau distance \cite{arxiv:0908.4094}.
 
   Other distances include the Ulam distance \cite{doi:10.1515/dma.1992.2.3.241}.
 
+  Linear programming bounds for permutation codes have been derived \cite{arxiv:1912.04500}.
+
 notes:
   - 'Review of parallels between linear binary codes and permutation groups \cite{doi:10.1016/j.ejc.2009.03.044}.'
 
 features:
   rate: 'Asymptotically good codes in the Ulam metric exist \cite{arxiv:2401.17235}.'
 
+
 relations:
   parents:
     - code_id: group_classical
       detail: 'Codes in permutations are group-alphabet codes for the symmetric group \(G=S_n\).'
+    - code_id: symmetric_space
+      detail: 'The permutation group can be viewed as a finite symmetric space \(G/H\) with \(G = S_n \times S_n\) and \(H=S_n\) \cite{doi:10.1006/eujc.1998.0272,arxiv:1912.04500}\cite[Table 3]{arxiv:1007.2905}.'
   cousins:
     - code_id: convolutional
       detail: 'Convolutional codes in permutations have been constructed \cite{doi:10.1109/TCOMM.2005.858683}.'
diff --git a/codes/classical/groups/unitary/unitary.yml b/codes/classical/groups/unitary/unitary.yml
@@ -7,7 +7,7 @@ code_id: unitary
 physical: groups
 
 name: 'Unitary code'
-introduced: '\cite{arxiv:0806.2317,arxiv:0809.3813}'
+introduced: '\cite{arxiv:0809.3813}'
 
 description: |
   Encodes \(K\) states (codewords) into the unitary group \(U(N)\).
diff --git a/codes/classical/groups/unitary/unitary_design.yml b/codes/classical/groups/unitary/unitary_design.yml
@@ -14,7 +14,7 @@ description: |
   The design conditions are defined using the \(t\)th tensor product of the group's adjoint representation.
 
 protection: |
-  Bounds on design size have been computed \cite{arxiv:0806.2317}.
+  Bounds on design size have been computed \cite{arXiv:0809.3813}.
 
 
 relations:
diff --git a/codes/classical/homogeneous/homogeneous_space_classical.yml b/codes/classical/homogeneous/homogeneous_space_classical.yml
@@ -23,7 +23,9 @@ protection: |
   Functions on \(G/H\) that transform as an irrep of \(G\) are called \(G\)\textit{-harmonics}. 
 
   If the decomposition of a homogeneous space into \(G\)-irreps is \textit{multiplicity free}, there are no multiplicities, and the irreps and their internal indices are sufficient to completely label a basis for the space. 
-  For example, the integer angular momentum \(J\) and its \(z\)-axis projection \(m\) are sufficient to completely label the spherical harmonics (a.k.a. be a good set of quantum numbers), which in turn can be used to expand any function on the two-sphere \(S^2\).
+  In this case, the pair \((G,H)\) is called a Gelfand pair.
+  For example, the integer angular momentum \(J\) and its \(z\)-axis projection \(m\) are sufficient to completely label the spherical harmonics (a.k.a. be a good set of quantum numbers), which in turn can be used to expand any function on the two-sphere \(S^2 = SO(3)/SO(2)\). 
+  Therefore, \((SO(3),SO(2))\) is a Gelfand pair.
   
   Functions that correspond to projections onto irreps are called \textit{zonal spherical functions} \cite{doi:10.2307/1969252}; these correspond to functions on the double coset space \(H \backslash G / H\) \cite[Eq. (2.9)]{arxiv:math/0701533} and can be obtained by averaging harmonics over \(G\). 
   
diff --git a/codes/classical/homogeneous/symmetric/grassmann/grassmannian.yml b/codes/classical/homogeneous/symmetric/grassmann/grassmannian.yml
@@ -7,8 +7,8 @@ code_id: grassmannian
 physical: quotients
 
 name: 'Grassmannian code'
-introduced: '\cite{arxiv:math/0208002,arxiv:math/0208003,arxiv:math/0208004}'
-
+introduced: '\cite{arxiv:math/0208002,arxiv:math/0208003,arxiv:math/0208004,arxiv:0806.2317}'
+# Last ref for complex cases
 
 description: |
   Encodes \(K\) states (codewords) into a compact Grassmannian, which includes the real, complex, or quaternionic Grassmannians.
diff --git a/codes/classical/matrices/sum-rank-metric/rank-metric/gabidulin.yml b/codes/classical/matrices/sum-rank-metric/rank-metric/gabidulin.yml
diff --git a/codes/classical/matrices/sum-rank-metric/rank-metric/lrpc.yml b/codes/classical/matrices/sum-rank-metric/rank-metric/lrpc.yml
diff --git a/codes/classical/matrices/sum-rank-metric/rank-metric/maximum_rank_distance.yml b/codes/classical/matrices/sum-rank-metric/rank-metric/maximum_rank_distance.yml
diff --git a/codes/classical/matrices/sum-rank-metric/rank-metric/rank_metric.yml b/codes/classical/matrices/sum-rank-metric/rank-metric/rank_metric.yml
@@ -47,10 +47,15 @@ notes:
   - 'See Ref. \cite{arxiv:1410.1333} for a discussion of MacWilliams identities and the relationship between rank metric and Gabidulin codes.'
   - 'See Ref. \cite{doi:10.1017/9781009283403}\cite[Sec. 5]{preset:HPArray} for more details.'
 
+
 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}.'
+  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}.'
+
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/q-ary_digits/ag/varieties/grassmannian_variety.yml b/codes/classical/q-ary_digits/ag/varieties/grassmannian_variety.yml
@@ -8,7 +8,7 @@ physical: q-ary_digits
 logical: q-ary_digits
 
 name: 'Grassmannian evaluation code'
-introduced: '\cite{manual:{C. T. Ryan, An application of Grassmannian varieties to coding theory. Congr. Numer. 57 (1987) 257–271.},manual:{C.T. Ryan, Projective codes based on Grassmann varieties, Congr. Numer. 57, 273–279 (1987).},doi:10.1016/0166-218X(90)90112-P}'
+introduced: '\cite{manual:{C. T. Ryan, An application of Grassmannian varieties to coding theory. Congr. Numer. 57 (1987) 257–271.},manual:{C.T. Ryan, Projective codes based on Grassmann varieties, Congr. Numer. 57, 273–279 (1987).},doi:10.1016/0166-218X(90)90112-P,manual:{Nogin, D. Yu. "Codes associated to Grassmannians." Arithmetic, geometry and coding theory (Luminy, 1993) (2011): 145-154.}}'
 
 description: |
   Evaluation code of polynomials evaluated on points lying on a finite-field Grassmannian embedded into projective space using the Plucker embedding \cite{doi:10.1515/9783110811056.145,doi:10.1007/978-1-4939-3082-1}.
diff --git a/codes/classical/rings/over_zq/q-ary_over_zq.yml b/codes/classical/rings/over_zq/q-ary_over_zq.yml
@@ -13,7 +13,7 @@ description: 'A code encoding \(K\) states (codewords) in \(n\) coordinates over
 
 protection: |
   In addition to the Hamming distance, codes over \(\mathbb{Z}_q\) are also defined over the Lee metric \cite{doi:10.1109/TIT.1958.1057446}.
-  Code bounds exist under this metric \cite{doi:10.1080/01969728208927711}.
+  Linear programming bounds exist under this metric \cite{doi:10.1080/01969728208927711,doi:10.1007/3-540-19368-5_5}.
 
 
 notes:
@@ -25,7 +25,7 @@ relations:
   parents:
     - code_id: rings_into_rings
     - code_id: symmetric_space
-      detail: 'The space of \(q\)-ary codes over \(\mathbb{Z}_q\) under the Lee metric can be viewed as a finite symmetric space \(G/H\) with \(G = D_q \wr S_n\) \cite{doi:10.1080/01969728208927711}\cite[Table 3]{arxiv:1007.2905}.'
+      detail: 'The space of \(q\)-ary codes over \(\mathbb{Z}_q\) under the Lee metric can be viewed as a finite symmetric space \(G/H\) with \(G = D_q \wr S_n\) \cite{doi:10.1080/01969728208927711,doi:10.1007/3-540-19368-5_5}\cite[Table 3]{arxiv:1007.2905}.'
   cousins:
     - code_id: combinatorial_design
       detail: 'Optimal constant-weight codes over \(\mathbb{Z}_q\) can be constructed \cite{doi:10.1016/0012-365X(95)00333-R} from a generalization of combinatorial designs to \(q\)-ary alphabets \cite{doi:10.4153/CJM-1963-069-5,doi:10.1007/s10623-007-9130-1}.'
diff --git a/codes/classical/spherical/modulation/psk.yml b/codes/classical/spherical/modulation/psk.yml
@@ -29,10 +29,10 @@ realizations:
 
 relations:
   parents:
-    - code_id: polygon
-      detail: 'The PSK constellation forms a \(q\)-gon.'
     - code_id: polyphase
       detail: 'A polyphase code can be thought of as a concatenation of a \(q\)-ary outer code with a PSK inner code. When the outer code is trivial, the construction reduces to a PSK code.'
+    - code_id: polygon
+      detail: 'The PSK constellation forms a \(q\)-gon.'
     - code_id: modulation
       detail: 'PSK is a modulation whose constellation consists of points arranged equidistantly on a circle.'
   cousins:
