~

Author: valbert4

codes/classical/bits/ltc/binary_ltc.yml

@@ -15,7 +15,7 @@ description: |
   
   More technically, the code is a \((u,R)\)-LTC if the rows of its parity-check matrix \(H\in \mathbb{F}_2^{r\times n}\) have weight at most \(u\) and if
   \begin{align}
-    \frac{1}{r}|H x| \geq \frac{R}{n} D(x,C)
+    \frac{1}{r}\operatorname{wt}(H x) \geq \frac{R}{n} D(x,C)
   \end{align}
   holds for any bitstring \(x\), where \(D(x,C)\) is the Hamming distance between \(x\) and the closest codeword to \(x\) \cite[Def. 11]{arxiv:1911.03069}.
 

codes/classical/bits/tanner/ldpc.yml

@@ -71,7 +71,7 @@ relations:
       detail: 'The dual of an LDPC code has a sparse generator matrix and is called an LDGM code.'
     # also in ldgm
     - code_id: random
-      detail: 'LDPC codes are often constructed non-determinisitically.'
+      detail: 'LDPC codes are often constructed nondeterministically.'
     - code_id: hamiltonian
       detail: 'There are relations between LDPC codes and statistical mechanical models of spin glasses \cite{arxiv:cond-mat/0205051,doi:10.1093/acprof:oso/9780198570837.001.0001,doi:10.1093/acprof:oso/9780198509417.001.0001,doi:10.1017/9781009283403}.'
 

codes/classical/matrices/subspace/subspace.yml

@@ -11,7 +11,7 @@ introduced: '\cite{arXiv:cs/0703061,arxiv:0805.3824,arxiv:1103.3117}'
 
 
 description: |
-  A code that is a set of subspaces of \(\mathbb{F}_q^n\). Codewords are generator matrices of the subspaces in reduced-row echelon form, and distance is governed by various notions of subspace overlap.
+  A code that is a set of subspaces of \(\mathbb{F}_q^n\). Codewords are the subspaces themselves, often represented by generator matrices in reduced-row echelon form, and distance is governed by various notions of subspace overlap.
 
 protection: |
   Subspace codes are quantified with respect to the subspace distance \cite{arXiv:cs/0703061} or injection distance \cite{arxiv:0805.3824}.

codes/classical/q-ary_digits/ag/rm/projective_reed_muller.yml

@@ -12,9 +12,9 @@ short_name: 'PRM'
 introduced: '\cite{doi:10.1016/0012-365X(90)90155-B,doi:10.1109/18.104317}'
 
 description: |
-  GRM code for nonzero points \(\{\alpha_1,\cdots,\alpha_n\}\) with \(n=m+1\) whose leftmost nonzero coordinate is one, corresponding to an evaluation code of polynomials over projective coordinates.
+  Evaluation code obtained by evaluating homogeneous polynomials on the points of the projective space \(PG(m,q)\), equivalently on representatives of the nonzero vectors in \(\mathbb{F}_q^{m+1}\) whose leftmost nonzero coordinate is one.
 
-  PRM codes include the codes PRM\(_q(r,m)\) for \(r<q\), which are are injective evaluation codes with parameters \cite{doi:10.1515/9783110811056.77}
+  PRM codes include the codes PRM\(_q(r,m)\) for \(r<q\), which are injective evaluation codes with parameters \cite{doi:10.1515/9783110811056.77}
   \begin{align}
     \left[ q^m+q^{m-1}\cdots +1, {m+r \choose r},(q+1-r)q^{m-1} \right]~.
   \end{align}

codes/classical/q-ary_digits/easy/q-ary_hamming.yml

@@ -29,7 +29,7 @@ relations:
     - code_id: small_distance
   cousins:
     - code_id: incidence_matrix
-      detail: 'Columns of a Hamming parity-check matrix correspond to 1D subspaces of \(\mathbb{F}_q^n\).'
+      detail: 'Columns of a Hamming parity-check matrix correspond to 1D subspaces of \(\mathbb{F}_q^r\).'
     - code_id: q-ary_cyclic
       detail: 'Hamming codes are equivalent to cyclic codes when \(q\) and \(r\) are relatively prime (\cite{preset:MacSlo}, pg. 194).'
     - code_id: bch

codes/classical/q-ary_digits/tanner/q-ary_ldpc.yml

@@ -19,8 +19,8 @@ description: |
   Alternatively, a member of an infinite family of \([n,k,d]_q\) codes for which the number of nonzero entries in each row and column of the parity-check matrix are both bounded above by a constant as \(n\to\infty\).
 
   A \textit{parity check} is performed by taking the inner product of a row of the parity-check matrix with a codeword that has been affected by a noise channel.
-  A parity check yields either zero (no error) or a nonzero field element (error).
-  Despite the fact that there is more than one nonzero outcome, \(q>2g\)-ary linear codes with sparse parity-check matrices are also called LDPC codes.
+  A parity check yields either zero (a satisfied check) or a nonzero field element (an unsatisfied check).
+  Despite the fact that there is more than one nonzero outcome, \(q\)-ary linear codes with sparse parity-check matrices are also called LDPC codes.
 
 protection: |
   Non-binary cycle LDPC codes for \(q\geq 32\) can exhibit good performance \cite{doi:10.1109/ICC.2004.1312545,doi:10.1109/ITW.2007.4313042,doi:10.1109/TCOMM.2008.060527}.

scripts/checked_files.txt

@@ -502,3 +502,23 @@ codes/classical/bits/tanner/regular_tanner/regular_binary_tanner.yml
 /home/valbert/eczoo_data/codes/classical/bits/reed_muller/biorthogonal.yml
 /home/valbert/eczoo_data/codes/classical/properties/block/info_retrieval/pir.yml
 /home/valbert/eczoo_data/codes/classical/q-ary_digits/easy/q-ary_hamming.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/universally_optimal/delsarte_optimal_q-ary.yml
+/home/valbert/eczoo_data/codes/classical/spherical/lattice_shell/eseven_shell.yml
+/home/valbert/eczoo_data/codes/classical/properties/block/symmetry/reversible.yml
+/home/valbert/eczoo_data/codes/classical/bits/tanner/ldpc.yml
+/home/valbert/eczoo_data/codes/classical/spherical/numerical/annealing_spherical.yml
+/home/valbert/eczoo_data/codes/classical/spherical/polytope/4d/disphenoidal288cell.yml
+/home/valbert/eczoo_data/codes/classical/bits/nonlinear/sphere_packing/sloane_whitehead.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/group/cyclic/q-ary_quad_residue.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/dual/dual_additive.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/ag/residueAG/cartier.yml
+/home/valbert/eczoo_data/codes/classical/spherical/small/petersen_spherical.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/alternant/generalized_srivastava.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/poset/nrt.yml
+/home/valbert/eczoo_data/codes/classical/bits/nonlinear/gray_map/originals/kerdock.yml
+/home/valbert/eczoo_data/codes/classical/bits/easy/unary.yml
+/home/valbert/eczoo_data/codes/classical/bits/cyclic/quad_residue/self_dual_48_24_12.yml
+/home/valbert/eczoo_data/codes/classical/bits/nonlinear/constantin_rao.yml
+/home/valbert/eczoo_data/codes/classical/properties/block/block.yml
+/home/valbert/eczoo_data/codes/classical/bits/reed_muller/dual_hamming/repetition.yml
+/home/valbert/eczoo_data/codes/classical/q-ary_digits/ag/varieties/quadric.yml