39 citations · 50 across the 14 of their papers we have counts for
15 papers
Cayley Incidence Graphs
Arnbjörg Soffía Árnadóttir, Alexey Gordeev, Sabrina Lato +2
Evra, Feigon, Maurischat, and Parzanchevski (2023) introduced a biregular extension of Cayley graphs. In this paper, we reformulate their definition and provide some basic properti…
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…
Sparsity greedoids and pebble game algorithms for posets
Signe Lundqvist, Tovohery Randrianarisoa, Klara Stokes +1
We generalise a sparsity condition for hypergraphs and show a result relating sparseness of hypergraphs to the decomposition of a modified incidence graph into edge-disjoint forest…
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…
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…
A Geometric Approach to Rank Metric Codes and a Classification of Constant Weight Codes
Tovohery Hajatiana Randrianarisoa
In this work we develop a geometric approach to the study of rank metric codes. Using this method, we introduce a simpler definition for generalized rank weight of linear codes. We…
Coding Theory using Linear Complexity of Finite Sequences
Tovohery Randrianarisoa
We define a metric on using the linear complexity of finite sequences. We will then develop a coding theory for this metric. We will give a Singleton-like bound an…
A Decoding Algorithm for Rank Metric Codes
Tovohery Hajatiana Randrianarisoa
In this work we will present algorithms for decoding rank metric codes. First we will look at a new decoding algorithm for Gabidulin codes using the property of Dickson matrices co…
A decoding algorithm for Twisted Gabidulin codes
Tovohery Randrianarisoa, Joachim Rosenthal
In this work, we modify the decoding algorithm for subspace codes by Koetter and Kschischang to get a decoding algorithm for (generalized) twisted Gabidulin codes. The decoding alg…
On the Genericity of Maximum Rank Distance and Gabidulin Codes
Alessandro Neri, Anna-Lena Horlemann-Trautmann, Tovohery Randrianarisoa +1
We consider linear rank-metric codes in . We show that the properties of being MRD (maximum rank distance) and non-Gabidulin are generic over the algebraic closu…
The number of matrices over with irreducible characteristic polynomial
Tovohery Hajatiana Randrianarisoa
Let be a finite field with elements. M. Gerstenhaber and Irving Reiner has given two different methods to show the number of matrices with a given characteristic…