Related papers: Perfect Codes for Uniform Chains Poset Metrics
Affine-invariant codes have attracted considerable attention due to their rich algebraic structure and strong theoretical properties. In this paper, we study a family of affine-invariant codes whose defining set consists of all descendants…
We present an algorithmic framework for computing anti-chains of maximum size in geometric posets. Specifically, posets in which the entities are geometric objects, where comparability of two entities is implicitly defined but can be…
S.Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529--563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs. We prove that each poset limit can be represented as a…
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…
In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set. We evaluate these rates…
Perfect difference families (PDFs for short) are important both in theoretical and in applications. Perfect difference matrices (PDMs for short) and the equivalent structure had been extensively studied and used to construct perfect…
A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.
We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency…
One-parameter criterion for 2-equipped posets with respect to cerepresentations is stated and proved. The list of sincere one-parameter 2-equipped posets is given as well as a complex matrix classification of all their indecomposables…
In a coherent category, the posets of subobjects have very strong properties. We emphasize the validity of these properties, in general categories, for well-behaved classes of subobjects. As an example of application, we investigate the…
We propose a simple algorithm generating labelled posets of given size according to the almost uniform distribution. By "almost uniform" we understand that the distribution of generated posets converges in total variation to the uniform…
In multi-parameter persistence, the matching distance is defined as the supremum of weighted bottleneck distances on the barcodes given by the restriction of persistence modules to lines with a positive slope. In the case of finitely…
This study investigates Hermitian rank-metric codes, a special class of rank-metric codes, focusing on perfect codes and on the analysis of their covering properties. Firstly, we establish bounds on the size of spheres in the space of…
As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli…
In this paper we consider codes in $\mathbb{F}_q^{s\times r}$ with packing radius $R$ regarding the NRT-metric (i.e. when the underlying poset is a disjoint union of chains with the same length) and we establish necessary condition on the…
Recently, Chang and Hyun obtained some classes of binary optimal codes via simplicial complexes. In this letter, we utilize posets of the disjoint union of two chains to construct binary optimal linear codes.
We study safe screening for metric learning. Distance metric learning can optimize a metric over a set of triplets, each one of which is defined by a pair of same class instances and an instance in a different class. However, the number of…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…