39 citations · 311 across the 30 of their papers we have counts for
6 papers · 1 filter
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…
Minimum Distance and the Minimum Weight Codewords of Schubert Codes
Sudhir R. Ghorpade, Prasant Singh
We consider linear codes associated to Schubert varieties in Grassmannians. A formula for the minimum distance of these codes was conjectured in 2000 and after having been establis…
Automorphism groups of Grassmann codes
Sudhir R. Ghorpade, Krishna V. Kaipa
We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the automorphism group of Grassmann codes. Further, we analyze the automorphisms of the…
Duals of Affine Grassmann Codes and their Relatives
Peter Beelen, Sudhir R. Ghorpade, Tom Hoeholdt
Affine Grassmann codes are a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. These codes were introduced in a recent work [2]. Here we consider…
Affine Grassmann Codes
Peter Beelen, Sudhir R. Ghorpade, Tom Hoeholdt
We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes…