From 785cfb81af1f2285e418adea5e211f040fc5b5e9 Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Sat, 13 Jul 2024 15:27:35 -0400 Subject: [PATCH] refs --- codes/classical/bits/nonlinear/constantin_rao.yml | 2 +- codes/classical/bits/nonlinear/vt_single_deletion.yml | 2 +- .../q-ary_digits/insertion_deletion/insertion_deletion.yml | 6 +++++- .../q-ary_digits/q-ary_digits_into_q-ary_digits.yml | 2 +- 4 files changed, 8 insertions(+), 4 deletions(-) diff --git a/codes/classical/bits/nonlinear/constantin_rao.yml b/codes/classical/bits/nonlinear/constantin_rao.yml index f113afee0..7db0eed02 100644 --- a/codes/classical/bits/nonlinear/constantin_rao.yml +++ b/codes/classical/bits/nonlinear/constantin_rao.yml @@ -26,7 +26,7 @@ protection: | 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}.' relations: diff --git a/codes/classical/bits/nonlinear/vt_single_deletion.yml b/codes/classical/bits/nonlinear/vt_single_deletion.yml index c8b0de0af..95a0c6be9 100644 --- a/codes/classical/bits/nonlinear/vt_single_deletion.yml +++ b/codes/classical/bits/nonlinear/vt_single_deletion.yml @@ -19,7 +19,7 @@ description: |- 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 \(a\).' diff --git a/codes/classical/q-ary_digits/insertion_deletion/insertion_deletion.yml b/codes/classical/q-ary_digits/insertion_deletion/insertion_deletion.yml index 70b79e01d..19a04f23e 100644 --- a/codes/classical/q-ary_digits/insertion_deletion/insertion_deletion.yml +++ b/codes/classical/q-ary_digits/insertion_deletion/insertion_deletion.yml @@ -28,7 +28,7 @@ protection: | # 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.' relations: @@ -37,6 +37,10 @@ relations: 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 diff --git a/codes/classical/q-ary_digits/q-ary_digits_into_q-ary_digits.yml b/codes/classical/q-ary_digits/q-ary_digits_into_q-ary_digits.yml index 784604481..bd0e8b786 100644 --- a/codes/classical/q-ary_digits/q-ary_digits_into_q-ary_digits.yml +++ b/codes/classical/q-ary_digits/q-ary_digits_into_q-ary_digits.yml @@ -37,7 +37,7 @@ protection: | 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: