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errorcorrectionzoo · Aug 1, 2024 · daf205b · daf205b
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diff --git a/codes/classical/bits/reed_muller/parity_check.yml b/codes/classical/bits/reed_muller/parity_check.yml
@@ -42,7 +42,6 @@ relations:
       detail: 'SPCs are RM\((m-1,m)\) codes.'
     - code_id: q-ary_parity_check
     - code_id: nearly_perfect
-    - code_id: mds
     - code_id: divisible
       detail: 'Binary SPCs are two-divisible.'
     - code_id: delsarte_optimal_q-ary

diff --git a/codes/classical/properties/block/distributed_storage/lrc/lcc.yml b/codes/classical/properties/block/distributed_storage/lrc/lcc.yml
@@ -22,8 +22,12 @@ description: |
 
   Modified versions of local correctability include \textit{relaxed local correctability} \cite{doi:10.4086/toc.2020.v016a018}.
 
+protection: |
+  Three-query LCCs have to have length that is superpolynomial in the message length \cite{arxiv:2311.00558}.
+
 notes:
   - 'See \href{https://www.cs.princeton.edu/~zdvir/LDCnotes/ldc-notes.html}{notes} by Z. Dvir and Ref. \cite{manual:{Gopi, Sivakanth. Locality in coding theory. Diss. Princeton University, 2018.}} for an introduction to LDCs and LCCs.'
+  - 'See popular summary of the result about three-query LCCs in \href{https://www.quantamagazine.org/magical-error-correction-scheme-proved-inherently-inefficient-20240109}{Quanta Magazine}.'
 
 
 relations:

diff --git a/codes/classical/q-ary_digits/orthogonal_array.yml b/codes/classical/q-ary_digits/orthogonal_array.yml
@@ -21,6 +21,7 @@ notes:
 relations:
   parents:
     - code_id: q-ary_digits_into_q-ary_digits
+      detail: 'There is a relation between \(q\)-ary codes and orthogonal arrays which is phrased in terms of the codes'' \hyperref[topic:weight-enumerator]{dual distance} \cite[Thm. 4.5]{doi:10.1016/S0019-9958(73)80007-5}\cite[Thm. 4.9]{doi:10.1007/978-1-4612-1478-6}.'
     - code_id: t-designs
       detail: 'Orthogonal arrays are designs on Hamming space \(GF(q)^n\) (a.k.a. the Hamming association scheme) \cite{manual:{Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973): vi+-97.},doi:10.1137/0134012,preset:LevBounds}\cite[Exam. 1]{doi:10.1109/18.720545}; see also Ref. \cite{arxiv:1302.4295}.'
   cousins:

diff --git a/codes/quantum/properties/block/topological/spt.yml b/codes/quantum/properties/block/topological/spt.yml
@@ -27,6 +27,9 @@ relations:
   parents:
     - code_id: topological
       detail: 'SPT codes realize symmetry-protected topological phases.'
+  cousins:
+    - code_id: bits_into_bits
+      detail: 'SPT orders may be used for encoding classical information \cite{arxiv:1407.3413}.'
 
 
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diff --git a/codes/quantum/qudits_galois/stabilizer/css/quantum_secret_sharing.yml b/codes/quantum/qudits_galois/stabilizer/css/quantum_secret_sharing.yml
@@ -32,6 +32,8 @@ relations:
       detail: 'Polynomial codes can be used for a specific construction of this code.'
     - code_id: reed_solomon
       detail: 'The classical information in this code is encoded using an RS code.'
+    - code_id: purity_testing
+      detail: 'The purity-testing protocol of Ref. \cite{arxiv:quant-ph/0205128} can be improved using approximate codes similar the approximate secret-sharing codes \cite{arxiv:0801.1544}.'
 
 
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