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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…
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…
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…
The Euler characteristic, -matroids, and a Möbius function
Trygve Johnsen, Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
We first give two new proofs of an old result that the reduced Euler characteristic of a matroid complex is equal to the Möbius number of the lattice of cycles of the matroid up to…
Weight Spectra of Gabidulin Rank-metric Codes and Betti Numbers
Trygve Johnsen, Rakhi Pratihar, Hugues Verdure
We consider -matroids and their associated classical matroids derived from Gabidulin rank-metric codes. We express the generalized rank weights of a Gabidulin rank-metric code i…
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…
Some Matroids Related to Sum-Rank Metric Codes
Avijit Panja, Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
We introduce the notion of sum-matroids and show its association with sum-rank metric codes. As a consequence, some results for sum-rank metric codes by Martínez-Peñas are generali…