Related papers: Outer Strong Blocking Sets
We consider a special family of SC-LDPC codes, that is, time-invariant LDPCC codes, which are known in the literature for a long time. Codes of this kind are usually designed by starting from QC block codes, and applying suitable unwrapping…
The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of $(n+1)$-element chains in the power…
Complex orthogonal designs (CODs) are used to construct space-time block codes. COD $\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p \times n$ matrix, where nonzero entries are filled by $\pm z_i$ or $\pm z^*_i$, $i = 1, 2,..., k$, such…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
Graph clustering is a central topic in unsupervised learning with a multitude of practical applications. In recent years, multi-view graph clustering has gained a lot of attention for its applicability to real-world instances where one has…
Design matrices are sparse matrices in which the supports of different columns intersect in a few positions. Such matrices come up naturally when studying problems involving point sets with many collinear triples. In this work we consider…
This paper revisits the set membership identification for linear control systems and establishes its convergence rates under relaxed assumptions on (i) the persistent excitation requirement and (ii) the system disturbances. In particular,…
We prove that approximating the size of stopping and trapping sets in Tanner graphs of linear block codes, and more restrictively, the class of low-density parity-check (LDPC) codes, is NP-hard. The ramifications of our findings are that…
In this paper we construct constant dimension space codes with prescribed minimum distance. There is an increased interest in space codes since a paper by Koetter and Kschischang were they gave an application in network coding. There is…
In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an…
We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result which shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a…
We consider three types of set-systems that have interesting applications in algebraic combinatorics and representation theory: maximal collections of the so-called strongly separated, weakly separated, and chord separated subsets of a set…
As a crucial technique for integrated circuits (IC) test response compaction, $X$-compact employs a special kind of codes called $X$-codes for reliable compressions of the test response in the presence of unknown logic values ($X$s). From a…
Optical orthogonal codes (OOCs) are sets of $(0,1)$-sequences with good auto- and cross-correlation properties. They were originally introduced for use in multi-access communication, particularly in the setting of optical CDMA…
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…
Coherent transport promises to be the basis for an emerging new technology. Notwithstanding, a mechanistic understanding of the fundamental principles behind optimal scattering media is still missing. Here, complex network analysis is…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The…