WebThe 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. 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.
Optimal Ferrers Diagram Rank-Metric Codes - IEEE Xplore
WebProblem 1 (Optimal Ferrers Diagram Rank-Metric Codes) Let Fbe an m nFerrers diagram, q 2 be a prime power, and be a positive integer, where n m. Does there exist an [F;k; ]R q rank-metric code C which attains the upper bound from Theorem 1? We want to find general code constructions, which provide optimal Ferrers diagram rank-metric codes for ... WebNov 15, 2024 · Four constructions for Ferrers diagram rank-metric (FDRM) codes are presented. The first one makes use of a characterization on generator matrices of a class … hovering flying insect
[1405.1885] Optimal Ferrers Diagram Rank-Metric Codes
WebMay 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. 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. … 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 … hovering golf cart