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Code distances of matrix rank-metric codes under Add-and-Remove transformations
Gianira N. Alfarano, Rakhi Pratihar, Adrien Vinçotte
For a matrix rank-metric code and an integer , the -th subcode distance of is the largest minimum rank distance of an -dimensional subcode of $…
Recursive decoding of binary rank Reed-Muller codes and Plotkin construction for matrix codes
Alain Couvreur, Rakhi Pratihar
In 2021, Augot, Couvreur, Lavauzelle and Neri introduced a new class of rank metric codes which can be regarded as rank metric counterparts of Reed-Muller codes. Given a finite Gal…
On the structure of the Schur squares of Twisted Generalized Reed-Solomon codes and application to cryptanalysis
Alain Couvreur, Rakhi Pratihar, Nihan Tanısalı +1
Twisted generalized Reed-Solomon (TGRS) codes constitute an interesting family of evaluation codes, containing a large class of maximum distance separable codes non-equivalent to g…
Decoding rank metric Reed-Muller codes
Alain Couvreur, Rakhi Pratihar
In this article, we investigate the decoding of the rank metric Reed--Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian…
Antipodal two-weight rank metric codes
Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
We consider the class of linear antipodal two-weight rank metric codes and discuss their properties and characterization in terms of -spreads. It is shown that the dimension of…
Constructions of optimal rank-metric codes from automorphisms of rational function fields
Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
We define a class of automorphisms of rational function fields of finite characteristic and employ these to construct different types of optimal linear rank-metric codes. The first…