Name
Abstract | ||
|---|---|---|
Motivated by notions from coding theory, we study the generalized minimum distance (GMD) function δI(d,r) of a graded ideal I in a polynomial ring over an arbitrary field using commutative algebraic methods. It is shown that δI is non-decreasing as a function of r and non-increasing as a function of d. For vanishing ideals over finite fields, we show that δI is strictly decreasing as a function of d until it stabilizes. We also study algebraic invariants of Geramita ideals. Those ideals are graded, unmixed, 1-dimensional and their associated primes are generated by linear forms. We also examine GMD functions of complete intersections and show some special cases of two conjectures of Tohăneanu–Van Tuyl and Eisenbud-Green-Harris. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.aam.2019.101940 | Advances in Applied Mathematics |
Keywords | Field | DocType |
primary,secondary | Invariant theory,Combinatorics,Finite field,Algebraic number,Commutative property,Polynomial ring,Pure mathematics,Coding theory,Mathematics | Journal |
Volume | ISSN | Citations |
112 | 0196-8858 | 0 |
PageRank | References | Authors |
0.34 | 0 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Susan M. Cooper | 1 | 0 | 0.34 |
| Alexandra Seceleanu | 2 | 0 | 1.69 |
| Stefan O. Tohaneanu | 3 | 0 | 0.34 |
| Maria Vaz Pinto | 4 | 18 | 3.02 |
| Rafael H. Villarreal | 5 | 75 | 15.69 |