Name
Title | ||
|---|---|---|
GMD functions for scheme-based linear codes and algebraic invariants of Geramita ideals. |
Abstract | ||
|---|---|---|
Motivated by notions from coding theory, we study the generalized minimum distance (GMD) function $delta_I(d,r)$ of a graded ideal $I$ in a polynomial ring over an arbitrary field using commutative algebraic methods. It is shown that $delta_I$ 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 $delta_I$ 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 Tohu{a}neanu--Van Tuyl and Eisenbud-Green-Harris. |
Year | Venue | DocType |
|---|---|---|
2018 | arXiv: Commutative Algebra | Journal |
Volume | Citations | PageRank |
abs/1812.06529 | 0 | 0.34 |
References | Authors | |
7 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Susan M. Cooper | 1 | 0 | 0.34 |
| Alexandra Seceleanu | 2 | 0 | 1.69 |
| Stefan O. Tohaneanu | 3 | 15 | 5.03 |
| Maria Vaz Pinto | 4 | 18 | 3.02 |
| Rafael H. Villarreal | 5 | 75 | 15.69 |