相关论文: Group divisible designs with block size five
High-rate space-time block codes (STBC with code rate > 1) in multi-input multi-output (MIMO) systems are able to provide both spatial multiplexing gain and diversity gain, but have high maximum likelihood (ML) decoding complexity. Since…
A regular-graph design is a block design for which a pair $\{a,b\}$ of distinct points occurs in $\lambda+1$ or $\lambda$ blocks depending on whether $\{a,b\}$ is or is not an edge of a given $\delta$-regular graph. Our paper describes a…
A \textbf{double-change covering design} (DCCD) is a $v$-set $V$ and an ordered list $\mathcal{L}$ of $b$ blocks of size $k$ where every pair from $V$ must occur in at least one block and each pair of consecutive blocks differs by exactly…
In this paper we study $b_5(n)$, the $5$-regular partitions of $n$. Using the theory of modular forms, we prove several theorems on the divisibility and distribution properties of $b_5(n)$ modulo prime $m\geq5$. In particular, we prove that…
The methods of classical invariant theory are used to construct generic polynomials for groups $S_5$ and $A_5$, along with explicit reductions to specializations of the generic polynomials defining any desired field extension with those…
We investigate a degree 5 invariant of groups of type E8 and give its applications to the structure of finite subgroups in algebraic groups.
Computational techniques for the construction of quasi-symmetric block designs are explored and applied to the case with $56$ points. One new $(56,16,18)$ and many new $(56,16,6)$ designs are discovered, and non-existence of $(56,12,9)$ and…
One of the most central and long-standing open questions in combinatorial design theory concerns the existence of Steiner t-designs for large values of t. Although in his classical 1987 paper, L. Teirlinck has shown that non-trivial…
We present GUT models based on an $SU(5)\times SU(5)$ GUT group. These models maintain the main successes of simple-group GUTs but permit simple solutions to the doublet-triplet splitting problem. Moreover, GUT breaking is triggered by…
Let $G$ be a simple algebraic group over an algebraically closed field $K$ with Lie algebra $\mathfrak{g}$. For unipotent elements $u \in G$ and nilpotent elements $e \in \mathfrak{g}$, the Jordan block sizes of $\operatorname{Ad}(u)$ and…
In this paper, we examine a class of doubly resolvable combinatorial objects. Let $t, k, \lambda, s$ and $v$ be nonnegative integers, and let $X$ be a set of $v$ symbols. A generalized Howell design, denoted $t$-$GHD_{k}(s,v;\lambda)$, is…
We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {\alpha; \beta; k; t}, where k is the number of information symbols, each codeword of an…
This paper considers two closely related concepts, mixed Steiner system and nonuniform group divisible design (GDD). The distinction between the two concepts is the minimum Hamming distance, which is required for mixed Steiner systems but…
We present a solution to the doublet-triplet splitting problem in supersymmetric $SU(5)$ by enlarging the group to $SU(5)\times SU(5)$ and by introducing two supermultiplets in the $(5,5)$ and $(\bar{5},\bar{5})$ representations of the…
We give a new construction of difference families generalizing Szekeres's difference families \cite{Sze}. As an immediate consequence, we obtain some new examples of difference families with several blocks in multiplicative subgroups of…
A $3$-$(v,\{4,6\},1)$ design is a configuration of $v$ points and a collection of $4$- and $6$-element subsets called blocks, that jointly contain every 3-element subset exactly once. Using an exhaustive computer search on $v\leq 28$ points…
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…
A $2$-$(v,k,\lambda)$ design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group $G$ in such a way that its block set is contained in (or coincides with) the set of all the zero-sum $k$-subsets of…
We find a five-parameter family of partial differential systems in two variables with two polynomial Hamiltonians. We give its symmetry and holomorphy conditions. These symmetries, holomorphy conditions and invariant divisors are new.
In this paper, we give a partial solution to a new isomorphism problem about $2$-$(v,k,k-1)$ designs from disjoint difference families in finite fields and Galois rings. Our results are obtained by carefully calculating and bounding some…