Rank-metric codes, linear sets, and their duality
نویسندگان
چکیده
منابع مشابه
Rank-metric codes and their duality theory
We compare the two duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of MacWilliams identities for the general case of Delsarte rank-metric codes, in a form that never appeared in the literature. The identities which we derive are very easy to handle, and allow us to re-establish in a very c...
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In this paper, we investigate the rank-metric codes which are proposed by Delsarte and Gabidulin to be complementary dual codes. We point out the relationship between Delsarte complementary dual codes and Gabidulin complementary dual codes. In finite field Fmq , we construct two classes of Gabidulin LCD MRD codes by self-dual basis (or almost self-dual basis) of Fmq over Fq. Under a suitable co...
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The State of Art for rank codes is represented. The theory and applications are considered.
متن کاملOn the List-Decodability of Random Linear Rank-Metric Codes
The list-decodability of random linear rank-metric codes is shown to match that of random rank-metric codes. Specifically, an Fq-linear rank-metric code over F m×n q of rate R = (1 − ρ)(1 − n m ρ) − ε is shown to be (with high probability) list-decodable up to fractional radius ρ ∈ (0, 1) with lists of size at most Cρ,q ε , where Cρ,q is a constant depending only on ρ and q. This matches the bo...
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This paper investigates general properties of codes with the rank metric. First, we investigate asymptotic packing properties of rank metric codes. Then, we study sphere covering properties of rank metric codes, derive bounds on their parameters, and investigate their asymptotic covering properties. Finally, we establish several identities that relate the rank weight distribution of a linear co...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2019
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-019-00703-z