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quantum glynn
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valbert4 committed Dec 13, 2023
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6 changes: 3 additions & 3 deletions codes/classical/q-ary_digits/easy/glynn.yml
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@@ -25,9 +25,9 @@ relations:
- code_id: reed_solomon
detail: 'The only other inequivalent \([10,5,6]_9\) code is a Reed-Solomon code \cite{manual:{T. Baicheva, I. Bouyukliev, S. Dodunekov, and W. Willems, “On the [10; 5; 6] Reed-Solomon and Glynn codes,” Mathematica Balkanica, New Series, vol. 18, pp. 67–78, 200}}.
It is the unique Euclidean self-dual code \cite{doi:10.1007/s10623-009-9267-1}.'
# - code_id: quantum_glynn
# detail: 'Applying the \hyperref[code:stabilizer_over_gfqsq]{Hermitian construction} to the Glynn code yields a \([[10,0,6]]_3\) quantum code \cite{arxiv:1502.05267}.
# The \([[9,1,5]]_3\) quantum Glynn code can be obtained by applying the \hyperref[code:stabilizer_over_gfqsq]{Hermitian construction} to the shortened Glynn code \cite[Corr. 4]{arxiv:1502.05267}.'
- code_id: quantum_glynn
detail: 'Applying the \hyperref[code:stabilizer_over_gfqsq]{Hermitian construction} to the Glynn code yields a \([[10,0,6]]_3\) quantum code \cite{arxiv:1502.05267,arxiv:1907.04391}.
The \([[9,1,5]]_3\) quantum Glynn code can be obtained by applying the \hyperref[code:stabilizer_over_gfqsq]{Hermitian construction} to the shortened Glynn code \cite[Corr. 4]{arxiv:1502.05267} (cf. \cite[Exam. 7]{arXiv:2108.08088}).'


# - code_id: cyclic
2 changes: 1 addition & 1 deletion codes/quantum/qubits/small_distance/small/stab_11_1_5.yml
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@@ -21,7 +21,7 @@ protection: 'Smallest stabilizer code that protects against errors on any two qu

relations:
parents:
- code_id: qubit_stabilizer
- code_id: stabilizer_over_gf4
- code_id: small_distance_quantum


33 changes: 33 additions & 0 deletions codes/quantum/qudits/small/stab_9_1_5.yml
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#######################################################
## This is a code entry in the error correction zoo. ##
## https://github.com/errorcorrectionzoo ##
#######################################################

code_id: stab_9_1_5
physical: qudits
logical: qudits

name: '\([[9,1,5]]_3\) quantum Glynn code'
short_name: '\([[9,1,5]]_3\)'
introduced: '\cite{arXiv:1502.05267}'

description: |
Nine-qutrit pure stabilizer code that is the smallest qutrit stabilizer code to correct two-qutrit errors.
See \cite[Exam. 7]{arXiv:2108.08088} for its stabilizer generator matrix.
protection: 'Smallest stabilizer code that protects against errors on any two qutrits. Detects four-qutrit errors.'


relations:
parents:
- code_id: stabilizer_over_gfqsq
- code_id: small_distance_quantum


# Begin Entry Meta Information
_meta:
# Change log - most recent first
changelog:
- user_id: VictorVAlbert
date: '2023-11-26'

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