gemini lint

Author: valbert4

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

@@ -90,7 +90,7 @@ relations:
     - code_id: delsarte_optimal_q-ary
       detail: 'The dual \([23,11,8]\) even-weight subcode of the Golay code is a sharp configuration \cite[Table 12.1]{preset:HKSbounds}.'
     - code_id: spherical_design
-      detail: 'The dual of the Golay code forms a spherical 3-design under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite[Exam. 9.3]{doi:10.1007/BF03187604}.'
+      detail: 'The dual of the Golay code forms a spherical 3-design under the \hyperref[topic:antipodal_mapping]{antipodal mapping} \cite[Exam. 9.3]{doi:10.1007/BF03187604}.'
 
 
 # The Golay code can be constructed as a cyclic code with the generator polynomial \(x^{11} + x^{10} + x^6 + x^5 + x^4 + x^2 + 1\) over \(\mathbb{F}_2\).

codes/classical/bits/reed_muller/biorthogonal.yml

@@ -18,7 +18,7 @@ description: |
   A member of the family of first-order RM codes.
   Its codewords are the rows of the \(2^m\)-dimensional Hadamard matrix \(H\) and its negation \(-H\) with the mapping \(+1\to 0\) and \(-1\to 1\).
   The family is self-orthogonal for \(m \geq 3\) \cite{arxiv:2303.16729}.
-  They form a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping}.
+  They form a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal_mapping]{antipodal mapping}.
 
   The automorphism group of the code is \(GA(m,\mathbb{F}_2)\) \cite{preset:MacSlo}.
 
@@ -43,7 +43,7 @@ relations:
       detail: 'First-order RM codes are RM\((1,m)\) codes.'
   cousins:
     - code_id: biorthogonal_spherical
-      detail: 'Each first-order RM code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{preset:Forney03}\cite[pg. 19]{preset:EricZin}. In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.'
+      detail: 'Each first-order RM code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal_mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{preset:Forney03}\cite[pg. 19]{preset:EricZin}. In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.'
 
 
 # Begin Entry Meta Information

codes/classical/bits/reed_muller/dual_hamming/simplex.yml

@@ -21,7 +21,7 @@ description: |
 
   The columns of its generator matrix are in one-to-one correspondence with the elements of the projective space \(PG(m-1,2)\), with each column being a chosen representative of the corresponding element.
   Simplex codes saturate the Plotkin bound and hence have nonzero codewords all of the same weight, \(2^{m-1}\) \cite[Th. 11(a)]{preset:MacSlo}\cite[Thm. 1.10.5]{preset:HKSbasics}.
-  The codewords form a \((2^m,2^m+1)\) simplex spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping}.
+  The codewords form a \((2^m,2^m+1)\) simplex spherical code under the \hyperref[topic:antipodal_mapping]{antipodal mapping}.
 
   A punctured simplex code is known as a \textit{MacDonald code} \cite{doi:10.1147/rd.41.0043}, with parameters \([2^m-2^u,m,2^{m-1}-2^{u-1}]\) for \(u \leq m-1\) \cite{doi:10.1109/TIT.1975.1055315}.
 
@@ -56,7 +56,7 @@ relations:
     - code_id: dual
       detail: 'Hamming and simplex codes are dual to each other.'
     - code_id: simplex_spherical
-      detail: 'Binary simplex codes map to \((2^m,2^m+1)\) simplex spherical codes under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite[Sec. 6.5.2]{preset:Forney03}\cite[pg. 18]{preset:EricZin}. In other words, simplex (simplex spherical) codes form simplices in Hamming (Euclidean) space.'
+      detail: 'Binary simplex codes map to \((2^m,2^m+1)\) simplex spherical codes under the \hyperref[topic:antipodal_mapping]{antipodal mapping} \cite[Sec. 6.5.2]{preset:Forney03}\cite[pg. 18]{preset:EricZin}. In other words, simplex (simplex spherical) codes form simplices in Hamming (Euclidean) space.'
     - code_id: biorthogonal
       detail: 'First-order RM codes and simplex codes are interconvertible via shortening and lengthening \cite[pg. 31]{preset:MacSlo}. Punctured first-order RM codes and simplex codes are interconvertible via expurgation and augmentation \cite[pg. 31]{preset:MacSlo}.'
     - code_id: constant_weight

codes/classical/bits/reed_muller/dual_hamming/simplex734.yml

@@ -16,7 +16,7 @@ alternative_names:
 description: |
   Second-smallest nontrivial member of the simplex-code family.
   The columns of its generator matrix are in one-to-one correspondence with the elements of the projective space \(PG(2,2)\), with each column being a chosen representative of the corresponding element.
-  The codewords form a \((8,9)\) simplex spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping}.
+  The codewords form a \((8,9)\) simplex spherical code under the \hyperref[topic:antipodal_mapping]{antipodal mapping}.
   As a simplex code, it is equidistant: every nonzero codeword has Hamming weight \(4\).
 
   Its generator matrix is

codes/classical/bits/reed_muller/reed_muller.yml

@@ -87,7 +87,7 @@ relations:
 
 
 # - code_id: biorthogonal
-#   detail: 'An RM\((1,m)\) code maps to a \((2^m,2^{m+1})\) biorthogonal signal set under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{preset:Forney03}. This set is equivalent to the  biorthogonal code since all such codes are unique up to equivalence \cite[pg. 19]{preset:EricZin}.'
+#   detail: 'An RM\((1,m)\) code maps to a \((2^m,2^{m+1})\) biorthogonal signal set under the \hyperref[topic:antipodal_mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{preset:Forney03}. This set is equivalent to the  biorthogonal code since all such codes are unique up to equivalence \cite[pg. 19]{preset:EricZin}.'
 
   #cousins:
     # - code_id: hamming

codes/classical/properties/block/distributed_storage/ldc.yml

@@ -16,7 +16,7 @@ introduced: '\cite{doi:10.1145/335305.335315}'
 description: |
   Recall that a block code encodes a length-\(k\) message into a length-\(n\) codeword, which is then sent through a noise channel to yield a received word.
   Informally, an LDC is a block code for which one can recover any coordinate of the message from at most \(r\) coordinates of the received word (assuming the received word is within some tolerated corruption rate \(\delta\)).
-  Efficiency of the correction is quantified by the code's \textit{query complexity} \(r\), and correction is performed by sampling subsets of \(r\) bits.
+  Efficiency of the decoding is quantified by the code's \textit{query complexity} \(r\), and decoding is performed by sampling subsets of \(r\) bits.
 
   LDCs have applications in computational complexity theory and cryptography \cite[Sec. 17.4]{doi:10.1017/CBO9780511804090}\cite{doi:10.1561/0400000030,doi:10.1145/301250.301397,doi:10.1145/2993749.2993761}.
 
@@ -36,6 +36,8 @@ relations:
     - code_id: block
     - code_id: ecc_finite
   cousins:
+    - code_id: lcc
+      detail: 'LDCs and LCCs are closely related and often studied together; any family of LCCs can be converted to a family of LDCs whose rate differs by a constant \cite{arxiv:1611.06980}.'
     - code_id: ltc
       detail: 'There are relations between LDCs and LTCs \cite{doi:10.1007/978-3-642-15369-3_50}.'
     - code_id: quantum_locally_recoverable

codes/classical/spherical/group_orbit/slepian_group.yml

@@ -32,9 +32,9 @@ relations:
       detail: 'Slepian group-orbit codes are group-orbit codes on spheres.'
   cousins:
     - code_id: binary_linear
-      detail: 'Any length-\(n\) binary linear code can be used to define a diagonal subgroup of \(n\)-dimensional rotation matrices with \(\pm 1\) on the diagonals via the \hyperref[topic:antipodal-mapping]{antipodal mapping} \(0\to+1\) and \(1\to-1\). The orbit of this subgroup yields the corresponding Slepian group-orbit code; see \cite[Thm. 8.5.2]{preset:EricZin}.'
+      detail: 'Any length-\(n\) binary linear code can be used to define a diagonal subgroup of \(n\)-dimensional rotation matrices with \(\pm 1\) on the diagonals via the \hyperref[topic:antipodal_mapping]{antipodal mapping} \(0\to+1\) and \(1\to-1\). The orbit of this subgroup yields the corresponding Slepian group-orbit code; see \cite[Thm. 8.5.2]{preset:EricZin}.'
     - code_id: binary_antipodal
-      detail: 'Any length-\(n\) binary linear code can be used to define a diagonal subgroup of \(n\)-dimensional rotation matrices with \(\pm 1\) on the diagonals via the \hyperref[topic:antipodal-mapping]{antipodal mapping} \(0\to+1\) and \(1\to-1\). The orbit of this subgroup yields the corresponding Slepian group-orbit code; see \cite[Thm. 8.5.2]{preset:EricZin}.'
+      detail: 'Any length-\(n\) binary linear code can be used to define a diagonal subgroup of \(n\)-dimensional rotation matrices with \(\pm 1\) on the diagonals via the \hyperref[topic:antipodal_mapping]{antipodal mapping} \(0\to+1\) and \(1\to-1\). The orbit of this subgroup yields the corresponding Slepian group-orbit code; see \cite[Thm. 8.5.2]{preset:EricZin}.'
     - code_id: group_linear
       detail: 'Any finite-group code can be mapped to a Slepian group-orbit code by representing the group using orthogonal matrices \cite{doi:10.1109/18.104333}.'
 

codes/classical/spherical/modulation/bpsk.yml

@@ -35,7 +35,7 @@ relations:
     - code_id: psk
       detail: 'BPSK is also known as 2-PSK.'
     - code_id: binary_antipodal
-      detail: 'A binary antipodal code can be thought of as a concatenation of a binary outer code with a BPSK inner code. A single-bit binary code yields a spherical \((n,2,4)\) spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping}, which is equivalent to the BPSK code for dimension \(n=2\).'
+      detail: 'A binary antipodal code can be thought of as a concatenation of a binary outer code with a BPSK inner code. A single-bit binary code yields a spherical \((n,2,4)\) spherical code under the \hyperref[topic:antipodal_mapping]{antipodal mapping}, which is equivalent to the BPSK code for dimension \(n=2\).'
   cousins:
     - code_id: pam
       detail: 'BPSK for real \(\alpha\) is the simplest non-trivial PAM encoding.'

codes/classical/spherical/polytope/infinite/biorthogonal_spherical.yml

@@ -52,7 +52,7 @@ relations:
       detail: 'Orthoplexes and hypercubes are dual to each other. A suitable weighted union of the vertices of a hypercube and an orthoplex forms a weighted spherical 5-design in dimensions \(\geq 3\) \cite[Sec. 8.6, Ex. 5-2]{preset:Stroud71}\cite[Exam. 2.6]{arxiv:2403.07457}.'
     # Also in hypercube
     - code_id: binary_antipodal
-      detail: 'Each first-order RM\((1,m)\) code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{preset:Forney03}\cite[pg. 19]{preset:EricZin}. In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.'
+      detail: 'Each first-order RM\((1,m)\) code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal_mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{preset:Forney03}\cite[pg. 19]{preset:EricZin}. In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.'
     - code_id: antiprism
       detail: 'The antiprism reduces to the octahedron for \(q=3\).'
 

codes/classical/spherical/polytope/infinite/simplex_spherical/simplex_spherical.yml

@@ -44,7 +44,7 @@ relations:
     - code_id: dodecahedron
       detail: 'Vertices of a dodecahedron can be split up into vertices of five tetrahedra, which are simplex spherical codes for \(n=3\) \cite{preset:coxeter}.'
     - code_id: binary_antipodal
-      detail: 'Binary simplex codes map to \((2^m,2^m+1)\) simplex spherical codes under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite[Sec. 6.5.2]{preset:Forney03}\cite[pg. 18]{preset:EricZin}. In other words, simplex (simplex spherical) codes form simplices in Hamming (Euclidean) space.'
+      detail: 'Binary simplex codes map to \((2^m,2^m+1)\) simplex spherical codes under the \hyperref[topic:antipodal_mapping]{antipodal mapping} \cite[Sec. 6.5.2]{preset:Forney03}\cite[pg. 18]{preset:EricZin}. In other words, simplex (simplex spherical) codes form simplices in Hamming (Euclidean) space.'
     - code_id: antiprism
       detail: 'The antiprism reduces to the tetrahedron for \(q=2\).'