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Author: valbert4

codes/classical/bits/graph/incidence/petersen.yml

@@ -15,7 +15,7 @@ description: |
   The Petersen graph can be thought of as a dodecahedron with antipodes identified \cite[Appx. A.2.1]{arxiv:1703.07847}.
 
 notes:
-  - 'See more details, see \cite[Example 10.11.7]{doi:10.1007/978-3-540-72780-4}.'
+  - 'See \cite[Example 10.11.7]{doi:10.1007/978-3-540-72780-4} for more details.'
 
 relations:
   parents:

codes/classical/bits/tanner/regular_tanner/generalized_gallager.yml

@@ -13,7 +13,7 @@ introduced: '\cite{doi:10.1109/ICC.1999.767979}'
 
 description: |
   A LDPC code that generalizes the Gallager codes using the Tanner construction.
-  While Gallager code parity-check matrices consists of repetition code submatrices that are randomly permuted, generalized Gallager code matrices substitute general binary linear codes.
+  While Gallager-code parity-check matrices consist of repetition-code submatrices that are randomly permuted, generalized Gallager-code matrices instead use more general binary linear component codes.
 
 
 relations:

codes/classical/matrices/array/array.yml

@@ -22,9 +22,9 @@ description: |
 protection: |
   Since they are designed to protect against corruption of nodes in a distributed storage network, many array codes are analyzed in terms of their erasure capabilities.
 
-  An analogue of the Hamming metric for array codes comes from the Hamming distance between two codewords whose columns of length \(m\) are converted into values in \(\mathbb{F}_q^m\) by treating the latter as the \(m\)th \hyperref[topic:finite-fields]{extension} of \(\mathbb{F}_q\). 
-  This converts a matrix codeword over \(\mathbb{F}_q\) into a vector over \(\mathbb{F}_q^m\) and is called \textit{subpacketization}.
-  Linear array codes are those codes that are linear w.r.t. \(\mathbb{F}_q^m\), i.e., that are closed under addition and multiplication by elements of said field when in vector form.
+  An analogue of the Hamming metric for array codes comes from counting the number of column positions in which two codewords differ.
+  Equivalently, one may treat each length-\(m\) column as a single symbol from an alphabet of size \(q^m\); this interpretation underlies the subpacketization viewpoint.
+  Array codes are typically \(\mathbb{F}_q\)-linear as matrix codes. In some constructions, after choosing an identification of columns with symbols from an extension field \(\mathbb{F}_{q^m}\), one also obtains an \(\mathbb{F}_{q^m}\)-linear code.
 
   There are other notions of distance for array codes, including the rank metric and its generalization the sum-rank metric.
 

codes/classical/properties/block/symmetry/cyclic/cyclic.yml

@@ -19,8 +19,7 @@ relations:
       detail: 'Constacyclic codes with \(\alpha=1\) are cyclic.'
     - code_id: skew_cyclic
       detail: 'Skew-cyclic codes with \(\theta\) trivial are cyclic.'
-    - code_id: group_orbit
-      detail: 'All codewords of a cyclic code can be obtained from any codeword via cyclic shifts, meaning that the code consists of only one orbit.'
+
 
 # Begin Entry Meta Information
 _meta:

codes/classical/q-ary_digits/group/cyclic/q-ary_duadic.yml

@@ -11,7 +11,7 @@ name: '\(q\)-ary duadic code'
 introduced: '\cite{doi:10.1016/0097-3165(86)90066-X,doi:10.1007/978-3-7091-2786-5_1,doi:10.7907/CZA5-PX53,doi:10.1109/TIT.1987.1057300}'
 
 description: |
-  Member of a pair of cyclic linear binary codes that satisfy certain relations, depending on whether the pair is \textit{even-like} or \textit{odd-like} duadic.
+  Member of a pair of cyclic linear \(q\)-ary codes that satisfy certain relations, depending on whether the pair is \textit{even-like} or \textit{odd-like} duadic.
   Duadic codes exist only when \(q\) is a square modulo \(n\) \cite{doi:10.1007/978-3-7091-2786-5_1}.
 
   Duadic codes come in two pairs, an even-like duadic pair and an odd-like duadic pair. All codewords in the respective pairs are \textit{even-like}, i.e., \(\sum_i c_i = 0\), or \textit{odd-like}, i.e., \(\sum_i c_i \neq 0\). A code with all even-like (odd-like) codewords is called even-like (odd-like).

codes/classical/q-ary_digits/projective/q-ary_simplex.yml

@@ -39,7 +39,7 @@ relations:
     - code_id: projective_reed_muller
       detail: 'The \(q\)-ary simplex codes are first-order PRM codes \cite[Sec. 1.2.2]{doi:10.1007/978-94-011-3810-9}.'
     - code_id: incidence_matrix
-      detail: 'Columns of a simplex code''s generator matrix correspond to 1D subspaces of \(\mathbb{F}_q^n\).'
+      detail: 'Columns of a simplex code''s generator matrix correspond to 1D subspaces of \(\mathbb{F}_q^m\), i.e., to points of \(PG(m-1,q)\).'
     - code_id: griesmer
       detail: 'Simplex codes saturate the Griesmer bound (\cite{doi:10.1201/9781315371993}, Exer. 5.1.11).'
     - code_id: univ_opt_q-ary

codes/classical/spherical/group_orbit/sidelnikov.yml

@@ -11,7 +11,7 @@ name: 'Real-Clifford subgroup-orbit code'
 introduced: '\cite{manual:{V. M. Sidelnikov, On a finite group of matrices and codes on the Euclidean sphere (in Russian), Probl. Peredach. Inform. 33 (1997), 35–54 (1997); English translation in Problems Inform. Transmission 33 (1997), 29–44},doi:10.1109/ISIT.1997.613373}'
 
 description: |
-  Slepian group-orbit code of dimension \(2^r\), approximate asympotic size \(2.38 \cdot 2^{r(r+1)/2+1}\), and distance \(1\).
+  Slepian group-orbit code of dimension \(2^r\), approximate asymptotic size \(2.38 \cdot 2^{r(r+1)/2+1}\), and distance \(1\).
   Code is constructed by applying elements of an index-two subgroup of the \hyperref[topic:clifford]{real Clifford group}, when taken as a subgroup of the orthogonal group \cite{arxiv:math/0001038}, onto the vector \((1,0,0,\cdots,0)\).
   This group is the automorphism group of BW lattice, and the resulting codes coincide with the optimal spherical codes for dimensions \(\{4,8,16\}\).
 

scripts/checked_files.txt

@@ -399,3 +399,23 @@ codes/classical/bits/tanner/regular_tanner/regular_binary_tanner.yml
 /home/valbert/eczoo_data/codes/classical/bits/fountain/raptor.yml
 /home/valbert/eczoo_data/codes/classical/bits/tanner/irregular/ra/raa.yml
 /home/valbert/eczoo_data/codes/classical/spherical/modulation/ppm.yml
+/home/valbert/eczoo_data/codes/classical/matrices/array/mds_array/star.yml
+/home/valbert/eczoo_data/codes/classical/bits/cyclic/zetterberg.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/group/quasi_group.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/group/cyclic/q-ary_duadic.yml
+/home/valbert/eczoo_data/codes/classical/bits/tanner/irregular/ra/extended_ira.yml
+/home/valbert/eczoo_data/codes/classical/bits/tanner/regular_tanner/generalized_gallager.yml
+/home/valbert/eczoo_data/codes/classical/properties/block/symmetry/cyclic/cyclic.yml
+/home/valbert/eczoo_data/codes/classical/bits/nonlinear/gray_map/originals/nordstrom_robinson.yml
+/home/valbert/eczoo_data/codes/classical/bits/reed_muller/coxeter.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/projective/q-ary_simplex.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/ag/varieties/complete_intersections.yml
+/home/valbert/eczoo_data/codes/classical/bits/graph/incidence/petersen.yml
+/home/valbert/eczoo_data/codes/classical/properties/block/insertion_deletion/dna.yml
+/home/valbert/eczoo_data/codes/classical/properties/block/symmetry/skew_cyclic.yml
+/home/valbert/eczoo_data/codes/classical/properties/universally_optimal/delsarte_optimal.yml
+/home/valbert/eczoo_data/codes/classical/spherical/sharp_config/sharp_config.yml
+/home/valbert/eczoo_data/codes/classical/spherical/modulation/qpsk.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/group/quasi_group.yml
+/home/valbert/eczoo_data/codes/classical/spherical/group_orbit/sidelnikov.yml
+/home/valbert/eczoo_data/codes/classical/matrices/array/array.yml