39 citations · 311 across the 30 of their papers we have counts for
36 papers
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…
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…
Arithmetic, Geometry, and Coding Theory: Homage to Gilles Lachaud
Sudhir R. Ghorpade, Christophe Ritzenthaler, François Rodier +1
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many fac…
The Role of History in Learning and Teaching Mathematics: A Personal Perspective
Sudhir R. Ghorpade
This is a slightly revised version of the Presidential address (General) delivered at the 84th Annual Conference of the Indian Mathematical Society held at Jammu, India during Nove…
Pure Resolutions, Linear Codes, and Betti Numbers
Sudhir R. Ghorpade, Prasant Singh
We consider the minimal free resolutions of Stanley-Reisner rings associated to linear codes and give an intrinsic characterization of linear codes having a pure resolution. We use…
A Polymatroid Approach to Generalized Weights of Rank Metric Codes
Sudhir R. Ghorpade, Trygve Johnsen
We consider the notion of a -polymatroid, due to Shiromoto, and the more general notion of -demi-polymatroid, and show how generalized weights can be defined for them…