13. MRD codes: constructions and connections
J Sheekey, KU Schmidt, A Winterhof - Combinatorics and finite fields …, 2019 - degruyter.com
Rank-metric codes are codes consisting of matrices with entries in a finite field, with the
distance between two matrices being the rank of their difference. Codes with maximum size …
distance between two matrices being the rank of their difference. Codes with maximum size …
[HTML][HTML] Linear cutting blocking sets and minimal codes in the rank metric
This work investigates the structure of rank-metric codes in connection with concepts from
finite geometry, most notably the q-analogues of projective systems and blocking sets. We …
finite geometry, most notably the q-analogues of projective systems and blocking sets. We …
Scattered subspaces and related codes
G Zini, F Zullo - Designs, Codes and Cryptography, 2021 - Springer
After a seminal paper by Shekeey (Adv Math Commun 10 (3): 475-488, 2016), a connection
between maximum h-scattered F q-subspaces of V (r, qn) and maximum rank distance …
between maximum h-scattered F q-subspaces of V (r, qn) and maximum rank distance …
Connections between scattered linear sets and MRD-codes
O Polverino, F Zullo - arXiv preprint arXiv:2001.10067, 2020 - arxiv.org
The aim of this paper is to survey on the known results on maximum scattered linear sets
and MRD-codes. In particular, we investigate the link between these two areas. In" A new …
and MRD-codes. In particular, we investigate the link between these two areas. In" A new …
A geometric approach to rank metric codes and a classification of constant weight codes
TH Randrianarisoa - Designs, Codes and Cryptography, 2020 - Springer
In this work we develop a geometric approach to the study of rank metric codes. Using this
method, we introduce a simpler definition for generalized rank weight of linear codes. We …
method, we introduce a simpler definition for generalized rank weight of linear codes. We …
[HTML][HTML] MRD-codes arising from the trinomial xq+ xq3+ cxq5∈ Fq6 [x]
G Marino, M Montanucci, F Zullo - Linear Algebra and its Applications, 2020 - Elsevier
Abstract In [10], the existence of F q-linear MRD-codes of F q 6× 6, with dimension 12,
minimum distance 5 and left idealiser isomorphic to F q 6, defined by a trinomial of F q 6 [x] …
minimum distance 5 and left idealiser isomorphic to F q 6, defined by a trinomial of F q 6 [x] …
A Large Family of Maximum Scattered Linear Sets of and Their Associated MRD Codes
G Longobardi, G Marino, R Trombetti, Y Zhou - Combinatorica, 2023 - Springer
Linear sets in projective spaces over finite fields were introduced by Lunardon (Geom Dedic
75 (3): 245–261, 1999) and they play a central role in the study of blocking sets, semifields …
75 (3): 245–261, 1999) and they play a central role in the study of blocking sets, semifields …
A new family of maximum scattered linear sets in
We generalize the example of linear set presented by the last two authors in" Vertex
properties of maximum scattered linear sets of $\mathrm {PG}(1, q^ n) $"(2019) to a more …
properties of maximum scattered linear sets of $\mathrm {PG}(1, q^ n) $"(2019) to a more …
Extending two families of maximum rank distance codes
In this paper, we properly extend the family of rank-metric codes recently found by
Longobardi and Zanella (2021) and by Longobardi, Marino, Trombetti and Zhou (2021) …
Longobardi and Zanella (2021) and by Longobardi, Marino, Trombetti and Zhou (2021) …
[HTML][HTML] Scattered trinomials of Fq6 [X] in even characteristic
D Bartoli, G Longobardi, G Marino… - Finite Fields and Their …, 2024 - Elsevier
In recent years, several families of scattered polynomials have been investigated in the
literature. However, most of them only exist in odd characteristic. In [9],[24], the authors …
literature. However, most of them only exist in odd characteristic. In [9],[24], the authors …