Optimal ferrers diagram rank-metric codes
WebApr 3, 2024 · Optimal rank-metric codes in Ferrers diagrams can be used to construct good subspace codes. Such codes consist of matrices having zeros at certain fixed positions. … WebAbstract. In this paper, we survey the main known constructions of Ferrers diagram rank-metric codes, and establish new results on a related conjecture by Etzion and Silberstein. We also give a sharp lower bound on the dimension of linear rank-metric anticodes with a given profile. Combining our results with the multilevel construction, we ...
Optimal ferrers diagram rank-metric codes
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WebNov 15, 2024 · For a given m × n Ferrers diagram F, an [ F, k, δ] q Ferrers diagram rank-metric (FDRM) code, briefly an [ F, k, δ] q code, is an [ m × n, k, δ] q rank-metric code in which for each m × n matrix, all entries not in F are zero. If F is a full m × n diagram with mn dots, then its corresponding FDRM codes are just classical rank-metric codes. WebDec 30, 2024 · Lifted MRD codes are one type of building blocks for the echelon-Ferrers construction [ 5 ]. In order to generalize the lifted MRD codes construction, a new family of Ferrers diagram rank-metric codes was presented, and …
WebNov 15, 2024 · Four constructions for Ferrers diagram rank-metric (FDRM) codes are presented. The first one makes use of a characterization on of a class of systematic … WebThe Ferrers diagram rank metric code is a set of matrices having nonzero entries only at positionswheretheFerrersdiagramhasdotsandequippedwiththerankdistancemetric.For …
Web{"upper_bound_constraints": [{"parameter": "", "name": "trivial_3", "value": 3583232}, {"parameter": "", "name": "heinlein_ihringer_semidefinite_programming", "value ... WebThe existence of optimal Ferrers diagram rank-metric code has been proven for various pairs [F,d].(see [1, 19, 20, 27]). The following Lemma is a criterion for check the existence of optimal Ferrers diagram rank-metric code. Lemma 2.8 [7, 8] Let F be a k × n(k≥ n) Ferrers diagram and each of the rightmost d − 1 columns of F has at least k ...
WebAbstract: Optimal rank-metric codes in Ferrers diagrams can be used to construct good subspace codes. Such codes consist of matrices having zeros at certain fixed positions. …
WebAbstract: Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct … incisor tooth descriptionWebFerrers diagram rank metric $ d_S(U,W) $ subspace distance between codewords $ U $ and $ W $ $ d_S( \mathcal{C}) $ ... S. Liu, Y. Chang and T. Feng, Constructions for optimal Ferrers diagram rank-metric codes, IEEE Transactions on Information Theory, 65 (2024), 4115-4130. doi: 10.1109/TIT.2024 ... inbound services btWebMay 8, 2014 · Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct good codes in the projective space. First, we consider rank-metric anticodes and prove a code-anticode bound for Ferrers diagram rank-metric codes. incisor tooth drawing with labelsWebThe Ferrers diagram rank metric code is a set of matrices having nonzero entries only at positionswheretheFerrersdiagramhasdotsandequippedwiththerankdistancemetric.For agivenm×nFerrers diagramF, the triple [F,k,δ]R qdenotes a linear Ferrers diagram rank metric code in Fq[F]with minimum rank distanceδand dimensionk. inbound services agreementhttp://subspacecodes.uni-bayreuth.de/api/5/6/4/ incisor tooth on dogWebMay 8, 2014 · Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct … incisor trading okcupid meaningWeband Wachter-Zeh [4] investigated systematically Ferrers diagram rank-metric codes and established four constructions to obtain optimal codes. This paper continues the work in [4]. inbound share in snowflake