11 citations · 14 across the 6 of their papers we have counts for
6 papers
Maximal quadrics over finite fields and minimal codewords of projective Reed-Muller codes
Alain Couvreur, Rati Ludhani
We study the classification of minimal codewords of projective Reed-Muller codes of order . This problem is equivalent to identifying quadrics over finite fields whose set of ra…
The Random Variables of the DNA Coverage Depth Problem
Şeyma Bodur, Stefano Lia, Hiram H. López +3
DNA data storage systems encode digital data into DNA strands, enabling dense and durable storage. Efficient data retrieval depends on coverage depth, a key performance metric. We…
Projective Nullstellensatz for not necessarily algebraically closed fields
Rati Ludhani
The Nullstellensatz, proved by Hilbert in 1893, is a classical result that holds when the base field is algebraically closed. When the base field is finite, a version of Hilbert's…
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…
On the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes
Sudhir R. Ghorpade, Rati Ludhani
We give an alternative proof of the formula for the minimum distance of a projective Reed-Muller code of an arbitrary order. It leads to a complete characterization of the minimum…
On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes
Sudhir R. Ghorpade, Rati Ludhani
Following Johnsen and Verdure (2013), we can associate to any linear code an abstract simplicial complex and in turn, a Stanley-Reisner ring . The ring is a standard…