5 papers
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…
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…
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…
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…