Optimal ferrers diagram rank-metric codes
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. … Weband 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].
Optimal ferrers diagram rank-metric codes
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WebFerrers 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 ... 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 ...
http://arxiv-export3.library.cornell.edu/abs/1405.1885v1 http://subspacecodes.uni-bayreuth.de/api/5/6/4/
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 are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct …
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.
WebJan 1, 2024 · Rank metric codes in Ferrers diagrams can be used to construct good subspace codes and constant dimension codes. In this paper, three constructions of … navy primary training aircraftmarks and spencer menswear fleecesWebThe 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. marks and spencer menswear jeansWebMay 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 … marks and spencer menswear saleWebJan 28, 2016 · Abstract: 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 … navy prims accessWeb{"upper_bound_constraints": [{"parameter": "", "name": "trivial_3", "value": 3583232}, {"parameter": "", "name": "heinlein_ihringer_semidefinite_programming", "value ... marks and spencer menswear knitwearWebOptimal 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 … marks and spencer menswear pyjamas