Symmetric rank codes
EM Gabidulin, NI Pilipchuk - Problems of Information Transmission, 2004 - Springer
… as a Kn-linear matrix code in the rank metric with maximum rank distance d = n and … codes
are called symmetric rank codes. In the vector representation, such codes are maximum rank …
are called symmetric rank codes. In the vector representation, such codes are maximum rank …
Higher-degree symmetric rank-metric codes
… codes can be seen as a special class of rank-metric codes. For \(d=… construction yields
symmetric Delsarte–Gabidulin codes, and … codes with the bounds inherited from the theory of rank-…
symmetric Delsarte–Gabidulin codes, and … codes with the bounds inherited from the theory of rank-…
On perfect symmetric rank-metric codes
U Mushrraf, F Zullo - arXiv preprint arXiv:2406.12450, 2024 - arxiv.org
… codes of odd order matrices and minimum distance three. Then we study the covering density
of a symmetric rank-metric code … we define families of symmetric rankmetric codes that are …
of a symmetric rank-metric code … we define families of symmetric rankmetric codes that are …
On codes correcting symmetric rank errors
NI Pilipchuk, EM Gabidulin - International Workshop on Coding and …, 2005 - Springer
… We study the capability of rank codes to correct so-called symmetric errors beyond the …
⊓⊔ In this case, the original code of rank distance 2 can correct symmetric errors of rank 1. …
⊓⊔ In this case, the original code of rank distance 2 can correct symmetric errors of rank 1. …
[HTML][HTML] Symmetric matrices and codes correcting rank errors beyond the⌊(d-1)/2⌋ bound
EM Gabidulin, NI Pilipchuk - Discrete applied mathematics, 2006 - Elsevier
… any matrix code, there exists a corresponding vector codes, … matrix codes containing a linear
subcode of symmetric … vector codes contain a linear subspace of so-called symmetric vectors…
subcode of symmetric … vector codes contain a linear subspace of so-called symmetric vectors…
On symmetric and Hermitian rank distance codes
A Cossidente, G Marino, F Pavese - Journal of Combinatorial Theory …, 2022 - Elsevier
… rank distance d r is a metric space. We investigate d–codes in ( M , d r ) and construct d–codes …
In the Hermitian case, we show the existence of an n–code of M , n even and n / 2 odd, of …
In the Hermitian case, we show the existence of an n–code of M , n even and n / 2 odd, of …
Maximum-rank array codes and their application to crisscross error correction
RM Roth - IEEE transactions on Information Theory, 1991 - ieeexplore.ieee.org
… This symmetry property of C(n,r) implies that if we regard the columns of each r E C(n, r )
as elements of @, with respect to the basis 4, the resulting [n,n - r ] conventional linear …
as elements of @, with respect to the basis 4, the resulting [n,n - r ] conventional linear …
Rank-metric codes and their duality theory
A Ravagnani - Designs, codes and Cryptography, 2016 - Springer
… maximum rank of a rank-metric code relate to the minimum and maximum rank of the dual
code, … 6 we study how the minimum and the maximum rank of a rank-metric code relate to the …
code, … 6 we study how the minimum and the maximum rank of a rank-metric code relate to the …
On equivalence of maximum additive symmetric rank-distance codes
Y Zhou - Designs, Codes and Cryptography, 2020 - Springer
… the rank-metric. However, by examples of symplectic semifields, it is already known that there
exist other maps preserving the rank-distance of maximum additive m-codes. … 2-codes in \({\…
exist other maps preserving the rank-distance of maximum additive m-codes. … 2-codes in \({\…
On Boolean functions, symmetric cryptography and algebraic coding theory
M Calderini - 2015 - iris.unitn.it
… index code is equivalent to finding the so-called min-rank … -rank notion to this more general
case, showing (Lemma 6.1.3) that is equal to the length of an optimal scalar linear index code…
case, showing (Lemma 6.1.3) that is equal to the length of an optimal scalar linear index code…