Rank-metric codes and their applications
The rank metric measures the distance between two matrices by the rank of their difference.
Codes designed for the rank metric have attracted considerable attention in recent years …
Codes designed for the rank metric have attracted considerable attention in recent years …
13. MRD codes: constructions and connections
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] Generalized twisted Gabidulin codes
G Lunardon, R Trombetti, Y Zhou - Journal of Combinatorial Theory, Series …, 2018 - Elsevier
Let C be a set of m by n matrices over F q such that the rank of A− B is at least d for all
distinct A, B∈ C. Suppose that m⩽ n. If# C= qn (m− d+ 1), then C is a maximum rank …
distinct A, B∈ C. Suppose that m⩽ n. If# C= qn (m− d+ 1), then C is a maximum rank …
Twisted linearized Reed-Solomon codes: A skew polynomial framework
A Neri - Journal of Algebra, 2022 - Elsevier
We provide an algebraic description for sum-rank metric codes, as quotient space of a skew
polynomial ring. This approach generalizes at the same time the skew group algebra setting …
polynomial ring. This approach generalizes at the same time the skew group algebra setting …
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 …
[HTML][HTML] MRD-codes arising from the trinomial xq+ xq3+ cxq5∈ Fq6 [x]
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] …
[HTML][HTML] Exceptional scattered polynomials
Let f be an F q-linear function over F q n. If the F q-subspace U={(xqt, f (x)): x∈ F qn} defines
a maximum scattered linear set, then we call fa scattered polynomial of index t. As these …
a maximum scattered linear set, then we call fa scattered polynomial of index t. As these …
New semifields and new MRD codes from skew polynomial rings
J Sheekey - Journal of the London Mathematical Society, 2020 - Wiley Online Library
In this article, we construct a new family of semifields, containing and extending two well‐
known families, namely Albert's generalised twisted fields and Petit's cyclic semifields (also …
known families, namely Albert's generalised twisted fields and Petit's cyclic semifields (also …
On the classification of exceptional scattered polynomials
Abstract Let f (X)∈ F qr [X] be a q-polynomial. If the F q-subspace U={(xqt, f (x))| x∈ F qn}
defines a maximum scattered linear set, then we call f (X) a scattered polynomial of index t …
defines a maximum scattered linear set, then we call f (X) a scattered polynomial of index t …
A New Family of MRD Codes in With Right and Middle Nuclei
R Trombetti, Y Zhou - IEEE Transactions on Information Theory, 2018 - ieeexplore.ieee.org
In this paper, we present a new family of maximum rank-distance (MRD) codes in of
minimum distance. In particular, when, we can show that the corresponding semifield is …
minimum distance. In particular, when, we can show that the corresponding semifield is …