traceability + frameproof + triangle surface

codes/classical/bits/nonlinear/gray_map/originals/kerdock.yml

@@ -28,9 +28,6 @@ features:
     - 'Complexity of soft decision decoding algorithm: \(4^m\) multiplications and \(m4^m\) additions \cite{doi:10.1109/18.312154,arxiv:math/0207208}.'
 
 
-realizations:
-  - 'Digital fingerprinting: \(t\)-collision secure schemes can be designed to detect a pirated copy once \(t\) users have colluded \cite{doi:10.1109/TIT.2004.838106}.'
-
 notes:
   - 'See corresponding MinT database entry \cite{manual:{Rudolf Schürer and Wolfgang Ch. Schmid. “Kerdock Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_CKerdock.html}}.'
 
@@ -54,6 +51,8 @@ relations:
       detail: 'Kerdock codes are asymptotically universally optimal \cite[Exam. 12.3.25]{doi:10.1201/9781315147901}.'
     - code_id: 24cell
       detail: 'The 24-cell is a special case of a family of codes for real projective planes, constructed using Kerdock codes \cite{manual:{Levenshtein, V. I. (1982). Bounds on the maximal cardinality of a code with bounded modulus of the inner product. In Soviet Math. Dokl (Vol. 25, No. 2, pp. 526-531).}} (cf. \cite{arXiv:1308.3188}).'
+# Morevoer, \(t\)-collision secure schemes can be designed to detect a pirated copy once \(t\) users have colluded '
+
 
 # - code_id: quaternary_over_z4
 #   detail: 'Kerdock codes can be seen, via the Gray map, as extended linear cyclic codes over \(\mathbb{Z}_4\), where the appended bit is a zero sum check \cite{doi:10.1109/18.312154,arxiv:math/0207208}.'

codes/classical/properties/block/copyright/frameproof.yml

@@ -0,0 +1,62 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: frameproof
+# binary and q-ary
+
+name: 'Frameproof Code'
+introduced: '\cite{doi:10.1007/3-540-44750-4_36,doi:10.1109/18.705568}'
+
+description: |
+  A block code designed to prevent a group of users from being able to collude to frame another user outside of the group for creating an unauthorized copy of data.
+  Even further, the group of users cannot frame a separate user even if they know the unique codeword of the separate user \cite{doi:10.1007/3-540-44750-4_36}.
+  Frameproof codes help to provide software protection from the illegal distribution and copying of computer software and copyrighted materials. These codes help protect products of distributors as well as other naive users from being framed of illegal activity \cite{doi:10.1007/3-540-44750-4_36}.
+
+  Separating codes are equivalent to codes with the secure frameproof property. A \(c\)\textit{-separating} code has the property that, for any two disjoint sets that each contain at most \(c\) code words, there is at least one position where the set of symbols of each set are disjoint \cite{doi:10.1007/s10623-021-00988-z}.
+
+  Let us define \(\Gamma = \{w^{(1)}, \dots, w^{(n)}\} \subseteq \{(0,1)\}^{l}\) as an ( \(l,n\) )-code.
+  Each codeword \(w^{(i)}\) correlates to a user \(u_i\).
+  Let \(C\) be a group of users.
+  A bit in position \(i\) is undetectable for the group \(C\) when the words assigned to the users in the group match at the the same position \(i\).
+  The feasible set of the group \(C\), denoted \(F(C;\Gamma)\) or \(F(C)\), for some user \(u \in C\) contains all of the codewords that match the groups set of undetectable bits.
+  Finally, if every subset \(S \subset \Gamma\) of size at most \(c\) satisfies \(F(S)\cap\Gamma = S\), then \(\Gamma\) is a \(c\)\textit{-frameproof} code \cite{doi:10.1007/3-540-44750-4_36}.
+
+  Any \(c\)-frameproof code must have at least length \(c\) \cite{doi:10.1007/3-540-44750-4_36}.
+  A length-\(l\) \(q\)-ary \(c\)-frameproof code has at most \(tq^{\lceil l/c \rceil} + O(q^{\lceil l/c \rceil - 1})\) codewords, where \(t\) is an integer between \(1\) and \(c\), and \(t \equiv 1\) modulo \(c\) \cite{doi:10.1137/S0895480101384633}.
+
+
+features:
+  rate: 'Frameproof codes tend to have large minimal distance and low rate \cite{doi:10.1007/3-540-44750-4_36}.
+  Specifically, for any positive integers \(n\) and \(c\), if \(l = 16c^{2}\log n\), then there exists a \(c\)-frameproof \( (l,n) \)-code which has rate \(n/l\) \cite{doi:10.1007/3-540-44750-4_36}.'
+
+
+realizations:
+  - 'Frameproof codes are utilized in digital fingerprinting and watermarking \cite{doi:10.1137/S0895480101384633}.'
+
+
+relations:
+  parents:
+    - code_id: ipp
+# detail: 'Codes with the identifiable parent property have the ability that given any descendent, a parent codeword can always be identified \cite{doi:10.1016/j.endm.2005.07.012}.'
+  cousins:
+    - code_id: traceability
+      detail: 'Frameproof codes fingerprint digital data and also they help prevent copyrighted information from unauthorized use \cite{arXiv:1411.5782}.
+      Codes with traceability also deter users from unauthorized copying or sharing of digital materials by being able to trace source of leaks, which also helps to ensure that an innocent user is not framed for the unauthorized activity \cite{doi:10.1109/18.841169}.'
+    - code_id: evaluation
+      detail: 'Asymptotic bounds on frameproof codes can be formulated using evaluation AG codes \cite{doi:10.1109/TIT.2002.804111,arXiv:1010.5764}.
+      A sufficient condition for an evaluation AG code to be frameproof can be recast as an instance of the Riemann-Roch equation \cite[Sec. 15.8.2]{doi:10.1201/9781315147901}.'
+    - code_id: kerdock
+      detail: 'Kerdock codes of sufficient order are separating \cite{manual:{Krasnopeev, A., and Yu L. Sagalovich. "The Kerdock codes and separating systems." Eight International Workshop on Algebraic and Combinatorial Coding Theory. Vol. 7. No. 7.2. 2002.},doi:10.1109/TIT.2004.838106}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: RaleyRoberts
+      date: '2024-03-15'
+    - user_id: VictorVAlbert
+      date: '2024-03-15'

codes/classical/q-ary_digits/ipp.yml → codes/classical/properties/block/copyright/ipp.yml

@@ -4,18 +4,18 @@
 #######################################################
 
 code_id: ipp
-physical: q-ary_digits
-logical: q-ary_digits
 
 name: 'Identifiable parent property (IPP) code'
 short_name: 'IPP'
 introduced: '\cite{doi:10.1006/jcta.1997.2851}'
 
-description: 'Stub.'
+description: |
+  A code with the ability that, given any descendent, a parent codeword can always be identified \cite{doi:10.1016/j.endm.2005.07.012}.
+
 
 relations:
   parents:
-    - code_id: q-ary_digits_into_q-ary_digits
+    - code_id: block
 
 
 # Begin Entry Meta Information

codes/classical/properties/block/copyright/traceability.yml

@@ -0,0 +1,62 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: traceability
+
+name: 'Traceability Codes'
+introduced: '\cite{doi:10.1109/18.841169}'
+
+description: |
+  A code that protects materials that have be copyrighted by providing the ability to trace potential leaks via combinatorial properties \cite{doi:10.1109/18.841169}.
+  The code also aids in helping to ensure that an innocent party cannot be framed for the pirated information \cite{doi:10.1109/18.915661}.
+  Having this ability will help to identify and disable pirates \cite{doi:10.1109/18.841169}.
+
+  Codes with strong traceability traces at least one member of a group that has constructed a pirate decoder \cite{doi:10.1109/18.915661}.
+  A pirate decoder is a generic pirate decryption process \cite{doi:10.1109/18.841169}.
+  A code with weak traceability has the ability to ensure that no group is able to frame another user \cite{doi:10.1109/18.915661}.
+
+
+features:
+  rate: |
+    Suppose \(n\) is the number of users, \(k\) is the number of users known by the pirates, and \(p\) is the probability that the pirates cannot be traced.
+    An open (public) resilient scheme using a hash function has the personal keys of the users consisting of \(O(k^{2}\log n)\) decryption keys which is the amount of decryptions needed to reveal the information.
+    The amount of data redundancy overhead is about \(O(k^{4}\log n)\) \cite{doi:10.1109/18.841169}.
+
+    A secret resilient scheme using a hash function has the personal keys of the users consisting of \(O(k \log(n/p))\) decryption keys, which is the amount of decryptions needed to reveal the information.
+    The amount of data redundancy overhead is about \(O(k^{2} \log(n/p))\) \cite{doi:10.1109/18.841169}.
+
+    A threshold (secret) scheme using a hash function that is successful against pirates which decrypt with probability \(> q\), has the personal keys of the users consisting of \((4k/3q)\log(n/p)\) decryption keys (note that this is the same as in the secret resilient schreme above).
+    These types of schemes only need order \(O(1)\) decryption operation performed by users to decrypt the information successfully.
+    Finally, the amount of data redundancy overhead is 4k encrypted keys which is a large improvement compared to the above \cite{doi:10.1109/18.841169}.
+
+  decoders:
+    - 'A pirate decoder represents the pirate decryption process that is considered a black box.
+    It is not necessary to know how it works so a pirate decode could be a physical box or even code on a computer \cite{doi:10.1109/18.841169}.'
+
+
+realizations:
+  - 'Code used in broadcast messages, pay-per-view movies, and protecting copyrighted online material \cite{doi:10.1109/18.915661}.'
+
+notes:
+  - 'Note that in the feature section above, the hash function maps the users into a set of 2k^{2} decryption keys \cite{doi:10.1109/18.841169}.'
+  - 'For code tables, see Refs. \cite{doi:10.1109/18.841169} and \cite{doi:10.1109/18.915661}.'
+  # - 'Fully resilient schemes guarantee to trace the source of any piracy \cite{doi:10.1109/18.841169}.'
+  # - 'Threshold schemes have a parameter of the scheme, say q, for which the scheme only traces sources of pirate decoders that decrypt with greater probability than q \cite{doi:10.1109/18.841169}.'
+  # - 'Secret schemes are those that have their decryption scheme and keys as secret. The open schemes are those that the decryption schemes and decryption keys are public information \cite{doi:10.1109/18.841169}.'
+
+relations:
+  parents:
+    - code_id: ipp
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: RaleyRoberts
+      date: '2024-03-15'
+    - user_id: VictorVAlbert
+      date: '2024-03-15'

codes/quantum/qubits/stabilizer/topological/color/stellated_color.yml

@@ -20,8 +20,8 @@ relations:
   parents:
     - code_id: color
   cousins:
-    - code_id: twist_defect_surface
-      detail: 'Stellated color codes are color-code analogues of twist-defect surface codes in that both encode logical information in lattice defects.
+    - code_id: triangle_surface
+      detail: 'Stellated color codes are color-code analogues of triangle surface codes in that both encode logical information in lattices with a single twist defect.
       Instances of the former can be obtained by fattening \cite{arxiv:cond-mat/0607736} the vertices of the latter \cite{arxiv:1806.02820}.'