Related papers: The existence of subspace designs
Explicit bases for the subfield subcodes of projective Reed-Muller codes over the projective plane and their duals are obtained. In particular, we provide a formula for the dimension of these codes. For the general case over the projective…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Despite great advances in computation, materials design is still science fiction. The construction of structure-property relations on the quantum scale will turn computational empiricism into true design.
Suppose the data consist of a set $S$ of points $x_j, 1 \leq j \leq J$, distributed in a bounded domain $D \subset R^N$, where $N$ and $J$ are large numbers. In this paper an algorithm is proposed for checking whether there exists a…
Most engineering models contain several parameters, and the map from input parameters to model output can be viewed as a multivariate function. An active subspace is a low-dimensional subspace of the space of inputs that explains the…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find…
In this paper, we initiate the study of constant dimension subspace codes restricted to Schubert varieties, which we call Schubert subspace codes. These codes have a very natural geometric description, as objects that we call intersecting…
We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
Over the past three decades, considerable effort has been devoted to the study of software architecture. A major portion of this effort has focused on the originally proposed view of four "C"s---components, connectors, configurations, and…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
In this short note we explain how to construct resolutions or regular alterations admitting an ample exceptional divisor, assuming the existence of projective resolutions or regular alterations. In particular, this implies the existence of…
Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.
The evolution of human intelligence led to the huge amount of data in the information space. Accessing and processing this data helps in finding solutions to applied problems based on finite-dimensional models. We argue, that formally, such…
In 1989, Ne\v{s}et\v{r}il and Pudl\'ak posed the following challenging question: Do planar posets have bounded Boolean dimension? We show that every poset with a planar cover graph and a unique minimal element has Boolean dimension at most…
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…
In this paper, we show that for all v\pmod 1 (mod 3), there exists a super- simple (v, 4, 2) directed design. Also, we show that for these parameters there exists a super-simple (v, 4, 2) directed design whose each defining set has at least…
This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…