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

Higher-degree symmetric rank-metric codes

A Bik, A Neri - SIAM Journal on Applied Algebra and Geometry, 2024 - SIAM
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-…

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 …

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. …

[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…

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 …

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 …

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 …

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 \({\…

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