相关论文: Strong difference families of special types
We compute the fundamental group of the complement of each irreducible sextic of weight eight or nine (in a sense, the largest groups for irreducible sextics), as well as of 169 of their derivatives (both of and not of torus type). We also…
Block codes, which correct asymmetric errors with limited-magnitude, are studied. These codes have been applied recently for error correction in flash memories. The codes will be represented by lattices and the constructions will be based…
We exhibit an explicit family $\mathcal{B}$ of $30$ subsets (``blocks'') of size $6$ of $[60]=\{1,2,\dots,60\}$ with the following property: for every $6$-subset $S\subset[60]$, there exists a block $B\in\mathcal{B}$ such that $|S\cap B|\ge…
We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+\delta$. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) case, we prove that…
Some sharp Bessel type inequalities for non-orthonormal families of vectors in inner product spaces are given. Applications for complex numbers are also provided.
Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…
In this paper, we generalize classical constructions of skew Hadamard difference families with two or four blocks in the additive groups of finite fields given by Szekeres (1969, 1971), Whiteman (1971) and Wallis-Whiteman (1972). In…
In this paper, we introduce several notions of "dimension" of a finite group, involving sizes of generating sets and certain configurations of maximal subgroups. We focus on the inequality $m(G) \leq \mathrm{MaxDim}(G)$, giving a family of…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
We study the class of indecomposable two-dimensional Landau-Ginzburg theories with (2,2) supersymmetry and central charge c < 6 with the aim of classifying all such theories up to marginal deformations. Our results include cases overlooked…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…
The classification of homogeneous scalar weighted shifts is known. Recently, Kor\'{a}nyi obtained a large class of inequivalent irreducible homogeneous bi-lateral $2$-by-$2$ block shifts. In this paper, we construct two distinct classes of…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a family of $p$-ary cyclic…
In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three…
We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^\alpha$ for a dense set of exponents $\alpha \in [2,\infty)$ and $r^n\log(r)$ for integers $n \geq 2$. The…
Combinatorial $t$-designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and $t$-designs has been…
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we…
We find a three-parameter family of ordinary differential systems in dimension six with affine Weyl group symmetry of type $D_4^{(2)}$. This is the second example which gave higher order Painlev\'e type systems of type $D_{4}^{(2)}$. We…
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…