From e19d6a5e615175db1b84846b7d8b037c2a30d2c1 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Fri, 23 Aug 2024 16:49:21 -0400 Subject: [PATCH] subspace refs --- .../classical/matrices/rank-metric/gabidulin.yml | 4 +++- .../q-ary_digits/projective/subspace.yml | 15 +++++++++++++-- 2 files changed, 16 insertions(+), 3 deletions(-) diff --git a/codes/classical/matrices/rank-metric/gabidulin.yml b/codes/classical/matrices/rank-metric/gabidulin.yml index ce418e09e..4fccbbde8 100644 --- a/codes/classical/matrices/rank-metric/gabidulin.yml +++ b/codes/classical/matrices/rank-metric/gabidulin.yml @@ -8,10 +8,12 @@ physical: matrices logical: matrices name: 'Gabidulin code' -introduced: '\cite{manual:{E. M. Gabidulin, \textit{Theory of Codes with Maximum Rank Distance}, Problemy Peredachi Informacii, Volume 21, Issue 1, \emph{3–16} (1985)},doi:10.1109/18.75248}' +introduced: '\cite{manual:{E. M. Gabidulin, \textit{Theory of Codes with Maximum Rank Distance}, Problemy Peredachi Informacii, Volume 21, Issue 1, \emph{3–16} (1985)},doi:10.1016/0097-3165(78)90015-8,doi:10.1109/18.75248}' alternative_names: - 'Vector rank-metric code' + - 'Delsarte-Gabidulin code' +#HKS Ch 29 description: | A linear code over \(GF(q^N)\) that corrects errors over rank metric instead of the traditional Hamming distance. Every element \(GF(q^N)\) can be written as an \(N\)-dimensional vector with coefficients in \(GF(q)\), and the rank of a set of elements is rank of the matrix formed by their coefficients. diff --git a/codes/classical/q-ary_digits/projective/subspace.yml b/codes/classical/q-ary_digits/projective/subspace.yml index fa26bc1ed..939c19cd6 100644 --- a/codes/classical/q-ary_digits/projective/subspace.yml +++ b/codes/classical/q-ary_digits/projective/subspace.yml @@ -14,14 +14,25 @@ description: | A code that is a set of subspaces of a projective space \(PG(n-1,q)\). protection: | - Subspace codes are quantified with respect to the subspace distance \cite{doi:10.1109/TIT.2008.926449}; see \cite{preset:HKSnetwork}. + Subspace codes are quantified with respect to the subspace distance \cite{doi:10.1109/TIT.2008.926449} or injection distance \cite{arxiv:0805.3824}.' + + Generalizations of various bounds for ordinary \(q\)-ary codes have been developed for subspace codes; see \cite{preset:HKSnetwork}. + +features: + decoding: + - 'List decoding up to the Singleton bound \cite{doi:10.1145/2488608.2488715}.' realizations: - - 'Wireless networks \cite{preset:HKSnetwork}.' + - 'Packet-based transmission over networks \cite{preset:HKSnetwork}.' relations: parents: - code_id: projective + cousins: + - code_id: gabidulin + detail: 'Gabidulin codes can be used to construct asymptotically good subspace codes \cite{doi:10.1109/TIT.2003.809567,doi:10.1109/TIT.2008.926449}.' + - code_id: rank_metric + detail: 'Subspace and rank-metric codes are closely related \cite{doi:10.1109/TIT.2008.928291}.' # Begin Entry Meta Information