Related papers: Near orders and codes
We give a general method to construct MDS one-dimensional convolutional codes. Our method generalizes previous constructions of H. Gluesing-Luerssen and B. Langfeld. Moreover we give a classification of one-dimensional Convolutional Goppa…
Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so called generalized toric codes. This extension consists on evaluating elements of an…
This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer…
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…
We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
Algebraic-geometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or,…
For a group $G$, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.
Using an algebraic approach based on the theory of Coxeter groups, we design, and describe the performance of, a class of line codes for parallel transmission of $b$ bits over $b+1$ wires that admit especially simple encoding and decoding…
Such large-structure tools of cohomology as toposes and derived categories stay close to arithmetic in practice, yet existing foundations for them go beyond the strong set theory ZFC. We formalize the practical insight by founding the…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
For a given second order elliptic operation $\mathcal{L}$ in a domain $\Omega\subset{\mathbb{R}}^\mathbf{N}$, $\mathbf{N}\ $, and a compact set $\mathbf{K}\subset\Omega$, order $\mathbf{N}$-$2$-Ahlfors-David regular, we define the space…
Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in $\SL(2,\ZZ)$. It is…
In this article we propose building general-purpose function approximators on top of Haar Scattering Networks. We advocate that this architecture enables a better comprehension of feature extraction, in addition to its implementation…
We give a constructive description of H{\"o}lder-like classes of functions on chord-arc curves in $\mathbb{R}^3$ in terms of a rate of approximation by harmonic functions in shrinking neighborhoods of those curve.
In coding theory, constructing codes with good parameters is one of the most important and fundamental problems. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes equal to prime powers.…
We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more…
In this work, we generalize the integer enumeration basis. We also construct bijections between the elements of special sets and the elements of some groups, and treat the special case of the hyperoctohedral groups. Then, we find a code…
In this paper, we introduce the concepts of gamma and beta approximations via general ordered topological approximation spaces. Also, increasing (decreasing) gamma and beta boundary, positive and negative regions are given in general…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…