1 citations · 1 across the 12 of their papers we have counts for
13 papers
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…
Betti Numbers and Higher Weight Spectra of Reed-Muller Codes
Sudhir R. Ghorpade, Trygve Johnsen, Rati Ludhani +1
We determine all the Betti numbers of the -ary second order Reed-Muller codes of length , and also of the elongations of matroids associated to these codes. We then use it…
A lattice framework for generalizing shellable complexes and matroids
Rakhi Pratihar, Tovohery H. Randrianarisoa, Klara Stokes
We introduce the notion of power lattices that unifies and extends the equicardinal geometric lattices, Cartesian products of subspace lattices, and multiset subset lattices, among…
Homotopy type of shellable -complexes and their homology groups
Sudhir R. Ghorpade, Rakhi Pratihar, Tovohery H. Randrianarisoa +2
The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for -simplicial complexes, r…
The Euler characteristic, -matroids, and a Möbius function
Trygve Johnsen, Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
We first give two new proofs of an old result that the reduced Euler characteristic of a matroid complex is equal to the Möbius number of the lattice of cycles of the matroid up to…
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…
Weight Spectra of Gabidulin Rank-metric Codes and Betti Numbers
Trygve Johnsen, Rakhi Pratihar, Hugues Verdure
We consider -matroids and their associated classical matroids derived from Gabidulin rank-metric codes. We express the generalized rank weights of a Gabidulin rank-metric code i…
Shellability and homology of -complexes and -matroids
Sudhir R. Ghorpade, Rakhi Pratihar, Tovohery H. Randrianarisoa
We consider a -analogue of abstract simplicial complexes, called -complexes, and discuss the notion of shellability for such complexes. It is shown that -complexes formed…
Some Matroids Related to Sum-Rank Metric Codes
Avijit Panja, Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
We introduce the notion of sum-matroids and show its association with sum-rank metric codes. As a consequence, some results for sum-rank metric codes by Martínez-Peñas are generali…
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…