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valbert4 committed Jul 13, 2024
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2 changes: 1 addition & 1 deletion codes/classical/bits/nonlinear/constantin_rao.yml
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features:
rate: |
CR codes for particular groups have higher rates than single-error-correcting codes under the binary asymmetric channel for all lengths except \(n = 2^r - 1\), in which case CR codes reduce to Hamming codes \cite{manual:{Kløve, Torleiv. Error correcting codes for the asymmetric channel. Department of Pure Mathematics, University of Bergen, 1981.}}; see Ref. \cite{arxiv:1310.7536}.
Size analysis is presented in Ref. \cite{doi:10.1016/S0019-9958(80)90082-0}.'
Size analysis is presented in Refs. \cite{doi:10.1016/S0019-9958(80)90082-0,doi:10.1109/18.651063}.'
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2 changes: 1 addition & 1 deletion codes/classical/bits/nonlinear/vt_single_deletion.yml
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C_{n,a}=\left\{x\in\{0,1\}^n: \sum_{i=1}^n i~x_i = a\mod (n+1) \right\}.
\end{align}
VT codes can be generalized to the \(q\)-ary case \cite{doi:10.1109/TIT.1984.1056962}.
VT codes can be generalized to the \(q\)-ary case \cite{arxiv:1708.04071,doi:10.1109/TIT.1984.1056962,arxiv:1906.07887}.
protection: 'Corrects a single asymmetric error (a \(0\) mapped to a \(1\)), a single deletion, or a single insertion of an arbitrary bit in an arbitrary position for any choice of \(a\).'

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# In the large alphabet setting, there exists a code which corrects a \(\delta\) fraction of insertions and deletions and has a rate of \((1-\Omega)^5\).'

notes:
- 'See Refs. \cite{doi:10.1109/TIT.2021.3056317}\cite[Sec. 22.7]{preset:HKSmetrics} for more details.'
- 'See Refs. \cite{arxiv:1906.07887,doi:10.1109/TIT.2021.3056317}\cite[Sec. 22.7]{preset:HKSmetrics} for more details.'


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cousins:
- code_id: permutation_invariant
detail: 'PI codes of distance \(d\) can protect against \(d-1\) (quantum) deletion errors.'
- code_id: combinatorial_design
detail: 'Perfect deletion correcting codes can be constructed using combinatorial design theory \cite{doi:10.1007/BF01390767,doi:10.1023/A:1008212622423}.'
- code_id: perfect
detail: 'Perfect deletion correcting codes can be constructed using combinatorial design theory \cite{doi:10.1007/BF01390767,doi:10.1023/A:1008212622423}.'


# Begin Entry Meta Information
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Other types of weight enumerators includes the Hamming weight enumerator, Lee weight enumerator, joint weight enumerator, split weight enumerator, and biweight enumerator \cite{preset:MacSlo}.
\end{defterm}
Noise channels include the symmetric noise channel, asymmetric noise channels \cite{manual:{Varshamov, R. R. "Some features of linear codes that correct asymmetric errors." Soviet Physics Doklady. Vol. 9. 1965.},doi:10.1109/TIT.1973.1054954,manual:{Kløve, Torleiv. Error correcting codes for the asymmetric channel. Department of Pure Mathematics, University of Bergen, 1981.}}, and insertion/deletion noise.
Noise channels include the symmetric noise channel, asymmetric noise channels \cite{manual:{Varshamov, R. R. "Some features of linear codes that correct asymmetric errors." Soviet Physics Doklady. Vol. 9. 1965.},doi:10.1109/TIT.1973.1054954,doi:10.1016/S0019-9958(79)90329-2,manual:{Kløve, Torleiv. Error correcting codes for the asymmetric channel. Department of Pure Mathematics, University of Bergen, 1981.}}, and insertion/deletion noise.
features:
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