Name
Title | ||
|---|---|---|
Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes |
Abstract | ||
|---|---|---|
We consider the question of determining the maximum number of points on sections of Grassmannians over finite fields by linear subvarieties of the Plucker projective space of a fixed codimension. This corresponds to a known open problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties. We recover most of the known results as well as prove some new results. A basic tool used is a characterization of decomposable subspaces of exterior powers, that is, subspaces in which every nonzero element is decomposable. Also, we use a generalization of the Griesmer-Wei bound that is proved here for arbitrary linear codes. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.ffa.2008.08.001 | Finite Fields and Their Applications |
Keywords | DocType | Volume |
linear error,plucker projective space,known result,grassmann code,decomposable subspaces,exterior power,grassmann variety,linear section,linear subvarieties,exterior algebra decomposable subspace grassmann variety linear code higher weight griesmer-wei bound grassmann code,complete weight hierarchy,basic tool,higher weight,arbitrary linear code,information theory,linear code,exterior algebra,error correction code,algebraic geometry | Journal | 15 |
Issue | ISSN | Citations |
1 | Finite Fields Appl. 15 (2009), no. 1, 54--68. | 20 |
PageRank | References | Authors |
1.95 | 6 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sudhir R. Ghorpade | 1 | 80 | 12.16 |
| Arunkumar R. Patil | 2 | 20 | 2.97 |
| Harish K. Pillai | 3 | 90 | 20.79 |