enjui edits

codes/classical/bits/cyclic/bch.yml

@@ -23,7 +23,7 @@ features:
     - 'Peterson decoder with runtime of order \(O(n^3)\) \cite{doi:10.1109/TIT.1960.1057586,manual:{S. Arimoto, "Encoding and decoding of p-ary group codes and the correction system," Information Processing in Japan (in Japanese), vol. 2, pp. 320-325, Nov. 1961.}} (see exposition in Ref. \cite{preset:Blahut}).'
     - 'Berlekamp-Massey decoder with runtime of order \(O(n^2)\) \cite{doi:10.1109/TIT.1969.1054260,preset:Berlekamp} and modification by Burton \cite{doi:10.1109/TIT.1971.1054655}; see also \cite{preset:PetersonWeldon,doi:10.1007/978-3-7091-2945-6}.'
     - 'Sugiyama et al. modification of the extended Euclidean algorithm \cite{doi:10.1016/S0019-9958(75)90090-X,doi:10.1017/CBO9780511606267}.'
-    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/SFCS.1998.743426}.'
+    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/18.782097,doi:10.1109/SFCS.1998.743426}.'
 
 notes:
   - 'See books \cite{preset:MacSlo,preset:LinCostello,doi:10.1017/CBO9780511807077} for expositions on BCH codes and code tables.'

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

@@ -17,7 +17,13 @@ description: |
   In alternative conventions (not used here), AG codes are restricted to be linear and/or include \hyperref[code:evaluation_varieties]{evaluation} codes defined using algebraic varieties more general than curves.
 
 features:
-  rate: 'Several sequences of linear AG codes beat the Gilbert-Varshamov bound and/or are asymptotically good \cite{doi:10.1007/BF01884295,doi:10.1006/jnth.1996.0147} (see Ref. \cite{preset:HPAlgCodes} for details). The rate of any linear AG code satisfies \begin{align} \frac{k}{n} \geq 1 - \frac{d}{n} - \frac{1}{\sqrt{q}-1}~, \end{align} which comes from the Drinfeld-Vladut bound \cite{manual:{S. G. Vlăduţ, V. G. Drinfeld, “Number of points of an algebraic curve”, Funktsional. Anal. i Prilozhen., 17:1 (1983), 68–69; Funct. Anal. Appl., 17:1 (1983), 53–54}}. Nonlinear AG codes can outperform this bound.'
+  rate: 'Several sequences of linear AG codes beat the Gilbert-Varshamov bound and/or are asymptotically good \cite{doi:10.1007/BF01884295,doi:10.1006/jnth.1996.0147} (see Ref. \cite{preset:HPAlgCodes} for details).
+  The rate of any linear AG code satisfies
+  \begin{align}
+    \frac{k}{n} \geq 1 - \frac{d}{n} - \frac{1}{\sqrt{q}-1}~,
+  \end{align}
+  which comes from the Drinfeld-Vladut bound \cite{manual:{S. G. Vlăduţ, V. G. Drinfeld, “Number of points of an algebraic curve”, Funktsional. Anal. i Prilozhen., 17:1 (1983), 68–69; Funct. Anal. Appl., 17:1 (1983), 53–54}}.
+  Nonlinear AG codes can outperform this bound.'
 
 notes:
   - 'See book by Goppa \cite{doi:10.1007/978-94-015-6870-8}.'

codes/classical/q-ary_digits/ag/evaluation.yml

@@ -9,8 +9,11 @@ logical: q-ary_digits
 
 name: 'Evaluation AG code'
 
+alternative_names:
+  - 'Function code'
+
 description: |
-  Also called a \textit{function code}. Evaluation code over \(GF(q)\) on a set of points \({\cal P} = \left( P_1,P_2,\cdots,P_n \right)\) in \(GF(q)\) lying on an algebraic curve \(\cal X\) whose corresponding vector space \(L\) of functions \(f\) consists of certain polynomials or rational functions. Codewords are evaluations of all functions at the specified points,
+  Evaluation code over \(GF(q)\) on a set of points \({\cal P} = \left( P_1,P_2,\cdots,P_n \right)\) in \(GF(q)\) lying on an algebraic curve \(\cal X\) whose corresponding vector space \(L\) of functions \(f\) consists of certain polynomials or rational functions. Codewords are evaluations of all functions at the specified points,
   \begin{align}
     \left( f(P_1), f(P_2), \cdots, f(P_n) \right) \quad\quad\forall f\in L~.
   \end{align}
@@ -48,6 +51,10 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: EnJuiKuo
+      date: '2024-03-18'
+    - user_id: VictorVAlbert
+      date: '2024-03-18'
     - user_id: VictorVAlbert
       date: '2022-08-11'
     - user_id: VictorVAlbert

codes/classical/q-ary_digits/ag/evaluationAG/elliptic.yml

@@ -12,6 +12,14 @@ name: 'Elliptic code'
 description: |
   Evaluation AG code of rational functions evaluated on points lying on an elliptic curve, i.e., a curve of genus one.
 
+
+# - 'The Elliptic Curve Cryptography covers all relevant asymmetric cryptographic primitives like digital signatures and key agreement algorithms \cite{doi:10.1109/WOSSPA.2011.5931464}.'
+#
+# - 'Application in Network security in cloud computing \cite{doi:10.1109/ICICV50876.2021.9388629}.'
+#
+# - 'RSA in electronic commerce (E-commerce) \cite{doi:10.1109/COMCAS.2017.8244805}.'
+
+
 relations:
   parents:
     - code_id: evaluation
@@ -25,5 +33,9 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: EnJuiKuo
+      date: '2024-03-18'
+    - user_id: VictorVAlbert
+      date: '2024-03-18'
     - user_id: VictorVAlbert
       date: '2022-07-20'

codes/classical/q-ary_digits/ag/residueAG/goppa.yml

@@ -24,7 +24,7 @@ features:
   decoders:
     - 'Algebraic decoding algorithms \cite{doi:10.1109/TIT.1975.1055350}. If \( \text{deg} G(x) = 2t \) , then there exists a \(t\)-correcting algebraic decoding algorithm for \( \Gamma(L,G) \).'
     - 'Sugiyama et al. modification of the extended Euclidean algorithm \cite{doi:10.1016/S0019-9958(75)90090-X,doi:10.1017/CBO9780511606267}.'
-    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/SFCS.1998.743426}.'
+    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/18.782097,doi:10.1109/SFCS.1998.743426}.'
     - 'Binary Goppa codes can be decoded using a RS-based decoder \cite{manual:{Daniel J. Bernstein, "Understanding binary-Goppa decoding." Cryptology ePrint Archive (2022).}}.'
 
 realizations:

codes/classical/q-ary_digits/ag/rs/alternant.yml

@@ -31,7 +31,7 @@ description: 'Given a length-\(n\) GRS code \(C\) over \(GF(q^m)\), an alternant
 features:
   decoders:
     - 'Variation of the Berlekamp-Welch algorithm \cite{doi:10.1109/TIT.1977.1055730}.'
-    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/SFCS.1998.743426}.'
+    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/18.782097,doi:10.1109/SFCS.1998.743426}.'
 
 notes:
   - 'See \cite[Ch. 12]{preset:MacSlo} for more details.'

codes/classical/q-ary_digits/ag/rs/generalized_reed_solomon.yml

@@ -25,7 +25,7 @@ features:
   decoders:
     - 'The decoding process of GRS codes reduces to the solution of a polynomial congruence equation, usually referred to as the key equation. Decoding schemes are based on applications of the Euclid algorithm to solve the key equation.'
     - 'Berlekamp-Massey decoder with runtime of order \(O(n^2)\) \cite{doi:10.1109/TIT.1968.1054109,doi:10.1109/TIT.1969.1054260,preset:Berlekamp}.'
-    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/SFCS.1998.743426} and modification by Koetter-Vardy for soft-decision decoding \cite{doi:10.1109/TIT.2003.819332}.'
+    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/18.782097,doi:10.1109/SFCS.1998.743426} and modification by Koetter-Vardy for soft-decision decoding \cite{doi:10.1109/TIT.2003.819332}.'
     - 'Hard-decision decoder for errors within the Singleton bound \cite{manual:{Berman, A., Dor, A., Shany, Y., Shapir, I., and Doubchak, A. (2023). U.S. Patent No. 11,855,658. Washington, DC: U.S. Patent and Trademark Office.}}.'
 
 realizations:

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

@@ -26,7 +26,7 @@ features:
     - 'Berlekamp-Massey decoder with runtime of order \(O(n^2)\) \cite{doi:10.1109/TIT.1968.1054109,doi:10.1109/TIT.1969.1054260,preset:Berlekamp} and modification by Burton \cite{doi:10.1109/TIT.1971.1054655}; see also \cite{preset:PetersonWeldon,doi:10.1007/978-3-7091-2945-6}.'
     - 'Gorenstein-Peterson-Zierler decoder with runtime of order \(O(n^3)\) \cite{doi:10.1109/TIT.1960.1057586,doi:10.1137/0109020} (see exposition in Ref. \cite{preset:Blahut}).'
     - 'Sugiyama et al. modification of the extended Euclidean algorithm \cite{doi:10.1016/S0019-9958(75)90090-X,doi:10.1017/CBO9780511606267}.'
-    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/SFCS.1998.743426} and modification by Koetter-Vardy for soft-decision decoding \cite{doi:10.1109/TIT.2003.819332}.'
+    - 'Guruswami-Sudan list decoder \cite{doi:10.1109/18.782097,doi:10.1109/SFCS.1998.743426} and modification by Koetter-Vardy for soft-decision decoding \cite{doi:10.1109/TIT.2003.819332}.'
 
 notes:
   - 'See books \cite{preset:MacSlo,preset:LinCostello,doi:10.1017/CBO9780511807077} for expositions on BCH codes and code tables.'

codes/quantum/qubits/small_distance/small/qubit_5_6_2.yml

@@ -13,7 +13,8 @@ introduced: '\cite{arXiv:quant-ph/9703002}'
 description: |
   Six-qubit cyclic CWS code detecting a single-qubit error.
 
-  This code is the smallest nontrivial member of the \(((5+2r,3\times 2^{2r+1},2))\) qubit code family \cite{arxiv:quant-ph/9704043} (see also \cite[Ex. 8]{arXiv:cs/0610159}\cite{arxiv:0801.0831}). This code is also a qubit member of the \(((n, 1+n(q-1),2))_q\) Galois-qudit code family \cite{arxiv:quant-ph/0210097}.
+  This code is the smallest nontrivial member of the \(((5+2r,3\times 2^{2r+1},2))\) qubit code family \cite{arxiv:quant-ph/9704043} (see also \cite[Ex. 8]{arXiv:cs/0610159}\cite{arxiv:0801.0831}).
+  This code is also a qubit member of the \(((n, 1+n(q-1),2))_q\) Galois-qudit code family \cite{arxiv:quant-ph/0210097}.
 
   Its codeword stabilizer consists of all cyclic shifts of \(ZXZII\).
   It's automorphism group is of size 3840 and given in Ref. \cite{arXiv:quant-ph/9703002} (see also \cite[Corr. 18]{arxiv:quant-ph/9704043}).

codes/quantum/qubits/small_distance/small/stab_5_1_3.yml

@@ -11,6 +11,9 @@ name: 'Five-qubit perfect code'
 short_name: '\([[5,1,3]]\)'
 introduced: '\cite{arXiv:quant-ph/9602019,arxiv:quant-ph/9604024}'
 
+alternative_names:
+  - 'Laflamme code'
+
 description: |
   Five-qubit cyclic stabilizer code that is the smallest qubit stabilizer code to correct a single-qubit error.
 
@@ -66,6 +69,8 @@ relations:
       detail: 'The five-qubit code is derived from the \([5,3,3]_4\) shortened hexacode via the \hyperref[code:stabilizer_over_gf4]{qubit Hermitian construction} \cite{arxiv:quant-ph/0310137}\cite[Exam. A]{arxiv:quant-ph/0511016}.'
     - code_id: quantum_mds
       detail: 'The five-qubit code is one of the two qubit quantum MDS codes.'
+    - code_id: frobenius
+      detail: 'The \([[5,1,3]]\) code is the smallest qubit Frobenius code \cite[Table I]{arxiv:1011.5814}.'
     - code_id: qudit_5_1_3
       detail: 'The \([[5,1,3]]_{\mathbb{Z}_q}\) modular-qudit code for \(q=2\) reduces to the five-qubit perfect code.'
     - code_id: galois_5_1_3

codes/quantum/qudits/frobenius.yml

@@ -10,26 +10,35 @@ logical: qudits
 name: 'Frobenius code'
 introduced: '\cite{arXiv:1011.5814}'
 
-description: 'Let \(C\) be a quantum cyclic code on \(n\) prime-dimensional qudits. \(C\) is a Frobenius code if there exists a positive integer \(t\) such that \(n\) divides \(p^t +1\).'
+description: |
+  A cyclic prime-qudit stabilizer code whose length \(n\) divides \(p^t + 1\) for some positive integer \(t\).
 
-protection: 'Protects against Pauli noise.'
+# Let \(C\) be a quantum cyclic code on \(n\) prime-dimensional qudits.
+# Then, \(C\) is a Frobenius code if there exists a positive integer \(t\) such that \(n\) divides \(p^t +1\).
+
+# protection: 'Protects against Pauli noise.'
 
 features:
   decoders:
     - 'Adapted from the Berlekamp decoding algorithm for classical BCH codes. There exists a polynomial time quantum algorithm to correct errors of weight at most \(\tau\), where \(\delta=2\tau+1\) is the BCH distance of the code \cite{arXiv:1011.5814}. '
 
 notes:
-  - 'Frobenius codes that are also stabilizer codes have been completely classified. No such codes exist when \(t\) is odd. All such codes with even \(t\) can be directly constructed.'
+  - 'Frobenius codes that are also stabilizer codes have been completely classified.
+  No such codes exist when \(t\) is odd.'
 
 relations:
   parents:
-    - code_id: qudits_into_qudits
+    - code_id: qudit_stabilizer
     - code_id: quantum_cyclic
 
 
 # Begin Entry Meta Information
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: EnJuiKuo
+      date: '2024-03-18'
+    - user_id: VictorVAlbert
+      date: '2024-03-18'
     - user_id: NolanCoble
       date: '2021-12-03'

users/users_db.yml

@@ -35,6 +35,11 @@
 
 #
 
+- user_id: EnJuiKuo
+  name: 'En-Jui Kuo'
+  githubusername: ericntunctu
+  gscholaruser: zLoWNsoAAAAJ
+
 - user_id: AdwayPatra
   name: 'Adway Patra'
   githubusername: adwayp007