stab_16_6_4, bbv, rdp, star, ye_barg, zigzag

codes/classical/matrices/raid/array.yml

@@ -17,7 +17,7 @@ alternative_names:
 description: |
   Matrix code over \(GF(q)\) designed for use in distributed storage, with the first such application being a RAID-type array of hard-drives such that information is protected against erasure of one or more hard drives.
   Each column of a matrix codeword is typically treated as a single codeword coordinate via subpacketization (defined below) and represents a large data block.
-  Array codes are denoted by \((n,k,m)\), where \(n\) is the number of nodes, \(k\) is the number of nodes needed to recover the data, and \(m\) is the column dimension of each codeword.
+  Array codes are denoted by \((n,k,m)\), where \(n\) is the number of nodes, \(k\) is the number of nodes needed to recover the data, and \(m\) is the column dimension of each codeword a.k.a. the subpacketization level.
 
 protection: |
   Since they are designed to protect against corruption of nodes in a distributed storage network, many array codes are analyzed in terms of their erasure capabilities.

codes/classical/matrices/raid/bbv.yml

@@ -0,0 +1,35 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: bbv
+physical: matrices
+
+
+name: 'Generalized EVENODD code'
+introduced: '\cite{doi:10.1109/18.485722}'
+
+alternative_names:
+  - 'Blaum-Bruck-Vardy array code'
+
+
+description: |
+  A generalization of the EVENODD code defined for parameters \(m\) and \(r\); see \cite{preset:HPArray}.
+
+
+relations:
+  parents:
+    - code_id: array
+  cousins:
+    - code_id: mds_array
+      detail: 'Generalized EVENODD codes for prime \(m\) and \(r=3\) are MDS array codes \cite{preset:HPArray}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-09-10'

codes/classical/matrices/raid/b_array.yml → codes/classical/matrices/raid/mds_array/b_array.yml

@@ -21,7 +21,8 @@ features:
 
 relations:
   parents:
-    - code_id: array
+    - code_id: mds_array
+      detail: 'B-codes are examples of MDS array codes \cite{arxiv:1112.0371}.'
   cousins:
     - code_id: reed_solomon
       detail: 'B-codes can be interpreted as RS codes over polynomials whose symbols lie in Galois rings \cite{doi:10.1109/18.179343,doi:10.1007/978-1-4615-1525-8_7}.'

codes/classical/matrices/raid/evenodd.yml → codes/classical/matrices/raid/mds_array/evenodd.yml

@@ -21,7 +21,10 @@ features:
 
 relations:
   parents:
-    - code_id: array
+    - code_id: bbv
+      detail: 'Generalized EVENODD codes reduce to EVENODD codes for \(r=2\) \cite{preset:HPArray}.'
+    - code_id: mds_array
+      detail: 'EVENODD codes are examples of MDS array codes \cite{arxiv:1112.0371}.'
 
 
 # Begin Entry Meta Information

codes/classical/matrices/raid/mds_array/rdp.yml

@@ -0,0 +1,30 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: rdp
+physical: matrices
+
+
+name: 'Row-Diagonal Parity (RDP) code'
+short_name: 'RDP'
+introduced: '\cite{manual:{Corbett, P., English, B., Goel, A., Grcanac, T., Kleiman, S., Leong, J., & Sankar, S. (2004, March). Row-diagonal parity for double disk failure correction. In Proceedings of the 3rd USENIX Conference on File and Storage Technologies (pp. 1-14).}}'
+
+
+description: |
+  An MDS array code protecting against double erasures.
+
+
+relations:
+  parents:
+    - code_id: mds_array
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-09-10'

codes/classical/matrices/raid/mds_array/star.yml

@@ -0,0 +1,29 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: star
+physical: matrices
+
+
+name: 'Star code'
+introduced: '\cite{doi:10.1109/TC.2007.70830}'
+
+
+description: |
+  An MDS array code protecting against triple erasures.
+
+
+relations:
+  parents:
+    - code_id: mds_array
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-09-10'

codes/classical/matrices/raid/x_array.yml → codes/classical/matrices/raid/mds_array/x_array.yml

@@ -17,7 +17,8 @@ description: |
 
 relations:
   parents:
-    - code_id: array
+    - code_id: mds_array
+      detail: 'X-codes are examples of MDS array codes \cite{arxiv:1112.0371}.'
 
 
 # Begin Entry Meta Information

codes/classical/matrices/raid/mds_array/ye_barg.yml

@@ -0,0 +1,29 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: ye_barg
+physical: matrices
+
+
+name: 'Ye-Barg code'
+introduced: '\cite{arxiv:1604.00454,arxiv:1605.08630}'
+
+
+description: |
+  An MDS array code with the optimal access property; see Ref. \cite{arxiv:1604.00454} for definitions.
+
+
+relations:
+  parents:
+    - code_id: mds_array
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-09-10'

codes/classical/matrices/raid/mds_array/zigzag.yml

@@ -0,0 +1,29 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: zigzag
+physical: matrices
+
+
+name: 'Zigzag code'
+introduced: '\cite{arxiv:1112.0371}'
+
+
+description: |
+  An MDS array code correcting against two erasures with optimal rebuilding ratio; see Ref. \cite{arxiv:1112.0371} for definitions.
+
+
+relations:
+  parents:
+    - code_id: mds_array
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-09-10'

codes/classical/matrices/regenerating/msr.yml

@@ -17,6 +17,8 @@ relations:
   parents:
     - code_id: regenerating
       detail: 'MSR codes are extreme points in the storage-bandwidth trade-off curve and are characterised by \(\alpha = (d-k+1)\beta\).'
+    - code_id: mds_array
+      detail: 'MSR codes are MDS array codes; e.g., see \cite{arxiv:2408.16584}.'
 
 
 # Begin Entry Meta Information

codes/classical/matrices/regenerating/regenerating.yml

@@ -42,6 +42,9 @@ relations:
   parents:
     - code_id: array
     - code_id: distributed_storage
+  cousins:
+    - code_id: locally_recoverable
+      detail: 'RGCs and LRCs are related via the group repair with optimal access problem \cite{arxiv:1605.08630}.'
 
 
 # Begin Entry Meta Information