narrow_sense_q-ary_bch

errorcorrectionzoo · Aug 19, 2024 · 0b608fc · 0b608fc
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diff --git a/codes/classical/bits/easy/hamming/hamming.yml b/codes/classical/bits/easy/hamming/hamming.yml
@@ -36,7 +36,7 @@ relations:
   parents:
     - code_id: perfect_binary
     - code_id: q-ary_hamming
-    - code_id: bch
+    - code_id: narrow_sense_q-ary_bch
       detail: 'Binary Hamming codes are binary primitive narrow-sense BCH codes \cite[Corr. 5.1.5]{doi:10.1017/CBO9780511807077}. Binary Hamming codes can be written in cyclic form \cite[Thm. 12.22]{preset:Hill}.'
     - code_id: lexicographic
       detail: 'Hamming codes are lexicodes \cite{doi:10.1109/TIT.1986.1057187}.'

diff --git a/...lassical/q-ary_digits/ag/rs/berlekamp.yml → ...assical/q-ary_digits/ag/grs/berlekamp.yml b/...lassical/q-ary_digits/ag/rs/berlekamp.yml → ...assical/q-ary_digits/ag/grs/berlekamp.yml
diff --git a/...-ary_digits/ag/rs/folded_reed_solomon.yml → ...ary_digits/ag/grs/folded_reed_solomon.yml b/...-ary_digits/ag/rs/folded_reed_solomon.yml → ...ary_digits/ag/grs/folded_reed_solomon.yml
diff --git a/...digits/ag/rs/generalized_reed_solomon.yml → ...igits/ag/grs/generalized_reed_solomon.yml b/...digits/ag/rs/generalized_reed_solomon.yml → ...igits/ag/grs/generalized_reed_solomon.yml
diff --git a/...digits/ag/rs/interleaved_reed_solomon.yml → ...igits/ag/grs/interleaved_reed_solomon.yml b/...digits/ag/rs/interleaved_reed_solomon.yml → ...igits/ag/grs/interleaved_reed_solomon.yml
diff --git a/...al/q-ary_digits/ag/rs/parvaresh_vardy.yml → ...l/q-ary_digits/ag/grs/parvaresh_vardy.yml b/...al/q-ary_digits/ag/rs/parvaresh_vardy.yml → ...l/q-ary_digits/ag/grs/parvaresh_vardy.yml
diff --git a/...ry_digits/ag/rs/extended_reed_solomon.yml → ...igits/ag/grs/rs/extended_reed_solomon.yml b/...ry_digits/ag/rs/extended_reed_solomon.yml → ...igits/ag/grs/rs/extended_reed_solomon.yml
diff --git a/...igits/ag/rs/narrow_sense_reed_solomon.yml → ...s/ag/grs/rs/narrow_sense_reed_solomon.yml b/...igits/ag/rs/narrow_sense_reed_solomon.yml → ...s/ag/grs/rs/narrow_sense_reed_solomon.yml
@@ -43,10 +43,4 @@ _meta:
   # Change log - most recent first
   changelog:
     - user_id: VictorVAlbert
-      date: '2022-08-12'
-    - user_id: VictorVAlbert
-      date: '2022-04-28'
-    - user_id: MustafaDoger
-      date: '2022-04-03'
-    - user_id: VictorVAlbert
-      date: '2021-10-29'
+      date: '2024-08-13'
diff --git a/...sical/q-ary_digits/ag/rs/reed_solomon.yml → ...l/q-ary_digits/ag/grs/rs/reed_solomon.yml b/...sical/q-ary_digits/ag/rs/reed_solomon.yml → ...l/q-ary_digits/ag/grs/rs/reed_solomon.yml
diff --git a/...classical/q-ary_digits/alternant/gbch.yml → ...sical/q-ary_digits/alternant/bch/gbch.yml b/...classical/q-ary_digits/alternant/gbch.yml → ...sical/q-ary_digits/alternant/bch/gbch.yml
diff --git a/codes/classical/q-ary_digits/alternant/bch/narrow_sense_q-ary_bch.yml b/codes/classical/q-ary_digits/alternant/bch/narrow_sense_q-ary_bch.yml
@@ -0,0 +1,30 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: narrow_sense_q-ary_bch
+physical: q-ary_digits
+logical: q-ary_digits
+
+name: 'Primitive narrow-sense BCH code'
+introduced: '\cite{doi:10.1137/0109020}'
+
+description: |
+  BCH codes for \(b=1\) and for \(n=q^r-1\) for some \(r\geq 2\).
+
+
+relations:
+  parents:
+    - code_id: q-ary_bch
+      detail: 'BCH codes are called narrow-sense when \(b=1\), and are called primitive when \(n=q^r-1\) for some \(r\geq 2\).'
+    - code_id: goppa
+      detail: 'Primitive narrow-sense BCH codes are Goppa codes with \(L=\{1,\alpha^{-1},\cdots,\alpha^{1-n}\}\) and \(G(x)=x^{\delta-1}\) \cite[pg. 522]{doi:10.1017/CBO9780511807077}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-08-13'
diff --git a/...ical/q-ary_digits/alternant/q-ary_bch.yml → .../q-ary_digits/alternant/bch/q-ary_bch.yml b/...ical/q-ary_digits/alternant/q-ary_bch.yml → .../q-ary_digits/alternant/bch/q-ary_bch.yml
@@ -46,8 +46,6 @@ relations:
   cousins:
     - code_id: reed_solomon
       detail: 'BCH codes are \hyperref[topic:finite-fields]{subfield} subcodes of RS codes.'
-    - code_id: goppa
-      detail: 'Narrow-sense BCH codes are Goppa codes with \(L=\{1,\alpha^{-1},\cdots,\alpha^{1-n}\}\) and \(G(x)=x^{\delta-1}\) \cite[pg. 522]{doi:10.1017/CBO9780511807077}.'
     - code_id: q-ary_ltc
       detail: 'Duals of BCH codes are locally testable \cite{doi:10.1109/SFCS.2005.16}.'
 

diff --git a/codes/quantum/qubits/stabilizer/data_syndrome.yml b/codes/quantum/qubits/stabilizer/data_syndrome.yml
@@ -52,7 +52,7 @@ relations:
       detail: 'The QDS code framework has been extended to quantum convolutional codes \cite{arxiv:1902.07395}.'
     - code_id: single_shot
       detail: 'QDS codes contain redundancy in their stabilizer generators so as to protect from syndrome measurement errors.'
-    - code_id: bch
+    - code_id: narrow_sense_q-ary_bch
       detail: 'Primitive narrow-sense BCH codes can be used as the syndrome measurement codes of a QDS code \cite{arxiv:2311.16044}.
       This construction requires fewer measurements than a previous general construction \cite{arxiv:1409.2559}.'
     - code_id: subsystem_stabilizer