ML p(r)ior | Minimum distance functions of complete intersections

Minimum distance functions of complete intersections

2016-01-28
We study the footprint function, with respect to a monomial order, of complete intersection graded ideals in a polynomial ring with coefficients in a field. For graded ideals of dimension one, whose initial ideal is a complete intersection, we give a formula for the footprint function and a sharp lower bound for the corresponding minimum distance function. This allows us to recover a formula for the minimum distance of an affine cartesian code and the fact that in this case the minimum distance and the footprint functions coincide. Then we present an extension of a result of Alon and F\"uredi, about coverings of the cube $\{0,1\}^n$ by affine hyperplanes, in terms of the regularity of a vanishing ideal.
PDF

Highlights - Most important sentences from the article

Login to like/save this paper, take notes and configure your recommendations

Related Articles

2019-04-01
1904.00702 | math.AG

Let $F(x, y) \in \mathbb{C}[x,y]$ be a polynomial of degree $d$ and let $G(x,y) \in \mathbb{C}[x,y]$… show more
PDF

Highlights - Most important sentences from the article

2019-04-08

We prove new barrier results in arithmetic complexity theory, showing severe limitations of natural … show more
PDF

Highlights - Most important sentences from the article

2017-06-01
1706.00313 | cs.IT

This paper is concerned with the construction of algebraic geometric codes defined from GGS curves. … show more
PDF

Highlights - Most important sentences from the article

2018-12-10

Let $G$ be a connected graph and let $\mathbb{X}$ be the set of projective points defined by the col… show more
PDF

Highlights - Most important sentences from the article

2018-12-20
1812.08590 | math.CO

In this paper we analyze the intersection between the norm-trace curve over $\mathbb{F}_{q^3}$ and t… show more
PDF

Highlights - Most important sentences from the article

2018-01-25
1801.08407 | cs.IT

We define a linear code $C_\eta(\delta_T,\delta_X)$ by evaluating polynomials of bidegree $(\delta_T… show more
PDF

Highlights - Most important sentences from the article

2017-07-09

Using commutative algebra methods we study the generalized minimum distance function (gmd function) … show more
PDF

Highlights - Most important sentences from the article

2018-11-07
1811.03491 | cs.LG

The degree-$d$ Chow parameters of a Boolean function $f: \{-1,1\}^n \to \mathbb{R}$ are its degree a… show more
PDF

Highlights - Most important sentences from the article

2017-12-03
1712.00747 | math.AG

Let $X$ be a complete simplicial toric variety over a finite field $\mathbb{F}_q$ with homogeneous c… show more
PDF

Highlights - Most important sentences from the article

2018-12-16

Motivated by notions from coding theory, we study the generalized minimum distance (GMD) function $\… show more
PDF

Highlights - Most important sentences from the article

2018-07-13
1807.05294 | cs.IT

This is a survey on weight enumerators, zeta functions and Riemann hypothesis for linear and algebra… show more
PDF

Highlights - Most important sentences from the article

2016-10-13

Elimination of unknowns in systems of equations, starting with Gaussian elimination, is a problem of… show more
PDF

Highlights - Most important sentences from the article

2018-10-09

It has been discovered that linear codes may be described by binomial ideals. This makes it possible… show more
PDF

Highlights - Most important sentences from the article

2018-09-28

In this paper, we study first the relationship between Pommaret bases and Hilbert series. Given a fi… show more
PDF

Highlights - Most important sentences from the article

2016-12-09

We consider the following multiplication-based tests to check if a given function $f: \mathbb{F}_q^n… show more
PDF

Highlights - Most important sentences from the article

2017-09-18

The well-known DeMillo-Lipton-Schwartz-Zippel lemma says that $n$-variate polynomials of total degre… show more
PDF

Highlights - Most important sentences from the article

</