4 papers
Enumeration of minimum weight codewords of affine Cartesian codes
Sakshi Dang, Sudhir R. Ghorpade
Affine Cartesian codes were first discussed by Geil and Thomsen in 2013 in a broader framework and were formally introduced by López, Rentería-Márquez and Villarreal in 2014. These…
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…
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…
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…