Related papers: Codes on Subgroups of Weighted Projective Tori
We show that every smooth toric variety (and many other algebraic spaces as well) can be realized as a moduli space for smooth, projective, polarized varieties. Some of these are not quasi--projective. This contradicts a recent paper…
We study toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of "K-motives". We explore the decomposition of certain toric varieties as K-motives into products of central simple…
Transfer maps and projection formulas are undoubtedly one of the key tools in the development and computation of (co)homology theories. In this note we develop an unified treatment of transfer maps and projection formulas in the…
A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements…
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…
In the present paper, we provide results that relate the Jacobi polynomials in genus $g$. We show that if a code is $t$-homogeneous that is, the codewords of the code for every given weight hold a $t$-design, then its Jacobi polynomial in…
In this paper, we introduce Jacobi polynomial generalizations of several classical invariants in coding theory over finite fields, specifically, the higher and extended weight enumerators, and we establish explicit correspondences between…
We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characterize when a subtorus action on such a toric variety admits a…
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
We characterise and investigate co-Higgs sheaves and associated algebraic and combinatorial invariants on toric varieties. In particular, we compute explicit examples.
In this review, novel non-standard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational…
This note presents a formula for the enumerative invariants of arbitrary genus in toric surfaces. The formula computes the number of curves of a given genus through a collection of generic points in the surface. The answer is given in terms…
In this article we investigate a class of linear error correcting codes in relation with the order polytopes. In particular we consider the order polytopes of tree posets and bipartite posets. We calculate the parameters of the associated…
We give a systematic construction of inverse-closed (Banach) subalgebras in general higher-dimensional non-commutative tori
We classify up to conjugacy the subgroups of certain types in the full, in the affine, and in the special affine Cremona groups. We prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results in the…
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for…
Linear codes with a few weights have wide applications in information security, data storage systems, consuming electronics and communication systems. Construction of the linear codes with a few weights and determination of their parameters…
Let $G = (V,E)$ be a simple graph. We investigate the Cohen-Macaulayness and algebraic invariants, such as the Castelnuovo-Mumford regularity and the projective dimension, of the toric ring $k[G]$ via those of toric rings associated to…
The paper presents a new cross-ratio of hypercomplex numbers based on projective geometry. We discuss the essential properties of the projective cross-ratio, notably its invariance under Mobius transformations. Applications to the geometry…