cascaded_reed_solomon

codes/classical/bits/reed_muller/reed_muller.yml

@@ -50,6 +50,8 @@ relations:
       detail: 'All RM codes can be constructed via the \((u|u+v)\) construction \cite[Ch. 13]{preset:MacSlo}.'
     - code_id: generalized_reed_muller
       detail: 'Binary GRM codes are RM codes.'
+    - code_id: cascaded_reed_solomon
+      detail: 'RM codes are special cases of hyperbolic evaluation codes \cite[Thm. 3 proof]{doi:10.1007/3-540-45624-4_17}.'
     - code_id: divisible
       detail: 'An RM\((r,m)\) code is \(2^{\left\lceil m/r\right\rceil-1}\)-divisible, according to McEliece''s theorem \cite{doi:10.1016/0097-3165(71)90066-5,doi:10.1016/0012-365X(72)90032-5}.'
     - code_id: group

codes/classical/properties/concatenated/generalized_concatenated.yml

@@ -8,6 +8,9 @@ code_id: generalized_concatenated
 name: 'Generalized concatenated code (GCC)'
 introduced: '\cite{manual:{È. L. Blokh, V. V. Zyablov, “Coding of Generalized Concatenated Codes”, Probl. Peredachi Inf., 10:3 (1974), 45–50; Problems Inform. Transmission, 10:3 (1974), 218–222},manual:{V. A. Zinoviev, “Generalized Cascade Codes”, Probl. Peredachi Inf., 12:1 (1976), 5–15; Problems Inform. Transmission, 12:1 (1976), 2–9}}'
 
+alternative_names:
+  - 'Cascade code'
+
 description: |
   A code that combines multiple outer codes of the same length and (possibly) different dimensions with a single inner code; see Refs. \cite{manual:{V. A. Zinoviev, “Generalized Cascade Codes”, Probl. Peredachi Inf., 12:1 (1976)}}\cite[Ch. 18]{preset:MacSlo}.
 

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

@@ -0,0 +1,37 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: cascaded_reed_solomon
+physical: q-ary_digits
+logical: q-ary_digits
+
+name: 'Hyperbolic evaluation code'
+introduced: '\cite{doi:10.1007/3-540-56686-4_51,doi:10.1109/18.476241,doi:10.1007/3-540-45624-4_17}'
+
+alternative_names:
+  - 'Hyperbolic cascaded RS code'
+
+description: |
+  An evaluation code over polynomials in two variables. 
+  Generator matrices are determined in Ref. \cite{doi:10.1007/3-540-45624-4_17} following initial formulations of the codes as generalized concatenations of RS codes \cite{doi:10.1007/3-540-56686-4_51,doi:10.1109/18.476241}; see \cite[Ex. 4.26]{doi:HPAlgCodes}. 
+
+protection: |
+  Minimum distance is determined by an order bound \cite{doi:10.1007/3-540-45624-4_17,doi:10.1109/18.825832}.
+
+
+relations:
+  parents:
+    - code_id: evaluation_polynomial
+  cousins:
+    - code_id: reed_solomon
+      detail: 'Hyperbolic evaluation codes were initially formulated as generalized concatenations (a.k.a. cascades) of RS codes \cite{doi:10.1007/3-540-56686-4_51,doi:10.1109/18.476241}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-08-17'