Rank-metric codeGabidulin codeConstant dimension codeSubspace codes, motivated by their extensive application in random network coding, have become one of central topics in algebraic coding theory during the last 10 years. Due to the significant application in subspace codes, Ferrers diagram rank-...
We associate a pair of q-polymatroids to a rank-metric codes and show that several invariants and structural properties of the code, such as generalized weights, the property of being MRD or an optimal anticode, and duality, are captured by the associated combinatorial object....
We define the rank-metric zeta function of a code as a generating function of its normalized $q$-binomial moments. We show that, as in the Hamming case, the zeta function gives a generating function for the weight enumerators of rank-metric codes. We further prove a functional equation and...
This [k×ℓ] matrix code is said to be linear if it is a subspace of Mk×ℓ(Fq). The rank distance between two k×ℓ matrices over Fq, say A and B, is defined by dR(A,B)= rank(A−B), and is clearly a metric. A [k×ℓ,δ] rank-metric code C is a [k×ℓ...
Marshall. New criteria for MRD and Gabidulin codes and some rank metric code constructions. arXiv:1507.08641 [cs, math], July 2015. arXiv: 1507.08641.Horlemann-Trautmann, A-L.; Marshall, K.: New criteria for MRD and Gabidulin codes and some Rank-Metric code constructions, Adv. Math. ...
We prove that the covering radius of the Reed-Muller code R(1, 9) in R(4, 9) is 240, not exceeding the quadratic bound. WB Vasantha,NS Babu - 《Ganita Sandesh》 被引量: 16发表: 1999年 Reed-Muller codes in the sum-rank metric We introduce the sum-rank metric analogue of Reed-...
Decoding of block and convolutional codes in rank metric Rank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. An optimal-cardinality algebraic code construction in rank metric was int... A...
We call a rank-metric code minimal if all its codewords have minimal rank support. Minimal rank-metric codes are the natural analogues (in the rank-metric) of minimal Hamming-metric codes, a class of objects that have been extensively studied in connection with finite geometry; see e.g. [...
We give an asymptotic equivalent of their average minimum rank distance and show that random $\\F{q}$-linear codes are on GV bound for rank metric. We show that the covering density of optimum codes whose codewords can be seen as square matrices is lower bounded by a function depending ...
Applications of rank-metric codes Definition Schemes based on rank codes appear in many areas of communications, cryptography, and information theory. Background The rank function defined on the set of matrices (or vectors) is in fact the norm function. The well-known inequalities for sums of ma...