Name
Abstract | ||
|---|---|---|
We determine the number of Fq-rational points of hyperplane sections of classical determinantal varieties defined by the vanishing of minors of a fixed size of a generic matrix, and identify the hyperplane sections giving the maximum number of Fq-rational points. Further we consider similar questions for sections by linear subvarieties of a fixed codimension in the ambient projective space. This is closely related to the study of linear codes associated to determinantal varieties, and the determination of their weight distribution, minimum distance, and generalized Hamming weights. The previously known results about these are generalized and expanded significantly. Connections to eigenvalues of certain association schemes, distance regular graphs, and rank metric codes are also indicated. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.disc.2020.111965 | Discrete Mathematics |
Keywords | Field | DocType |
Determinantal varieties,Linear codes,Weight distribution,Generalized Hamming weight,Association scheme,Rank metric codes | Codimension,Hamming code,Combinatorics,Finite field,Matrix (mathematics),Weight distribution,Hyperplane,Mathematics,Projective space | Journal |
Volume | Issue | ISSN |
343 | 9 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Beelen | 1 | 116 | 15.95 |
| Sudhir R. Ghorpade | 2 | 80 | 12.16 |