82 research outputs found
Stanley-Reisner resolution of constant weight linear codes
Given a constant weight linear code, we investigate its weight hierarchy and
the Stanley-Reisner resolution of its associated matroid regarded as a
simplicial complex. We also exhibit conditions on the higher weights sufficient
to conclude that the code is of constant weigh
Higher weight spectra of Veronese codes
We study q-ary linear codes C obtained from Veronese surfaces over finite
fields. We show how one can find the higher weight spectra of these codes, or
equivalently, the weight distribution of all extension codes of C over all
field extensions of the field with q elements. Our methods will be a study of
the Stanley-Reisner rings of a series of matroids associated to each code CComment: 14 page
A Polymatroid Approach to Generalized Weights of Rank Metric Codes
We consider the notion of a -polymatroid, due to Shiromoto, and the
more general notion of -demi-polymatroid, and show how generalized
weights can be defined for them. Further, we establish a duality for these
weights analogous to Wei duality for generalized Hamming weights of linear
codes. The corresponding results of Ravagnani for Delsarte rank metric codes,
and Martinez-Penas and Matsumoto for relative generalized rank weights are
derived as a consequence.Comment: 22 pages; with minor revisions in the previous versio
Toward Clemens' Conjecture in degrees between 10 and 24
We introduce and study a likely condition that implies the following form of
Clemens' conjecture in degrees between 10 and 24: given a general quintic
threefold in complex \IP^4, the Hilbert scheme of rational, smooth and
irreducible curves of degree on is finite, nonempty, and reduced;
moreover, each is embedded in with balanced normal sheaf
\O(-1)\oplus\O(-1), and in \IP^4 with maximal rank.Comment: Plain Tex, This eleven page paper is a joint manuscript, produced in
connection with the first author's participation in the conference "Geometry
and Physics", Zlatograd, Bulgaria, August 28 - Sept.2, 1995." This version
contains a small change in Remark (3.3); the hope expressed there has been
refine
A generalization of weight polynomials to matroids
Generalizing polynomials previously studied in the context of linear codes,
we define weight polynomials and an enumerator for a matroid . Our main
result is that these polynomials are determined by Betti numbers associated
with graded minimal free resolutions of the Stanley-Reisner ideals of and
so-called elongations of . Generalizing Greene's theorem from coding theory,
we show that the enumerator of a matroid is equivalent to its Tutte polynomial.Comment: 21 page
The cone of Betti diagrams of bigraded artinian modules of codimension two
We describe the positive cone generated by bigraded Betti diagrams of
artinian modules of codimension two, whose resolutions become pure of a given
type when taking total degrees. If the differences of these total degrees, p
and q, are relatively prime, the extremal rays are parametrised by order ideals
in N^2 contained in the region px + qy < (p-1)(q-1). We also consider some
examples concerning artinian modules of codimension three.Comment: 15 page
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