Related papers: Linear and Circular Single Change Covering Designs…
This paper focuses on controlling the absorbing set spectrum for a class of regular LDPC codes known as separable, circulant-based (SCB) codes. For a specified circulant matrix, SCB codes all share a common mother matrix, examples of which…
This paper studies circular designs for interference models, where a treatment assigned to a plot also affects its neighboring plots within a block. For the purpose of estimating total effects, the circular neighbor balanced design was…
A residual design ${\cal{D}}_B$ with respect to a block $B$ of a given design $\cal{D}$ is defined to be linearly embeddable over $GF(p)$ if the $p$-ranks of the incidence matrices of ${\cal{D}}_B$ and $\cal{D}$ differ by one. A sufficient…
A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points satisfying (i) every two blocks intersect each other in $\lambda$ points for a fixed $\lambda < v$ (ii) there…
In this paper, we investigate the problem of designing $(n, N; \mathcal{B})$-reconstruction codes for $N\in \{14,11,9,5\}$, where $\mathcal{B}$ is the single-deletion single-substitution ball function that maps a sequence to the set of all…
The subblock energy-constrained codes (SECCs) and sliding window-constrained codes (SWCCs) have recently attracted attention due to various applications in communcation systems such as simultaneous energy and information transfer. In a…
An $r$-block-coloring, simply $r$-coloring, of a Steiner triple system $\mathrm{STS}(v)$ is a partition of the block set into $r$ color classes, each color class being a partial parallel class. The chromatic index of $\mathrm{STS}(v)$,…
Additive CA on a cylinder of size $n$ can be represented by 01-string $V$ of length $n$ which is its rule. We study a problem: a class $S$ of rules given, for any $V\in S$ describe all sizes $n', n'>n,$ of cylinders such that extension of…
A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points such that every two blocks intersect each other in $\lambda$ points (and $\lambda < v$ is a fixed number) and…
The Kramer-Mesner method for constructing designs with a prescribed automorphism group $G$ has proven effective many times. In the special case of Steiner designs, the task reduces to solving an exact cover problem, with the advantage that…
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…
A sequence covering array, denoted \textsf{SCA}$(N;t,v)$, is a set of $N$ permutations of $\{0, \dots, v-1 \}$ such that each sequence of $t$ distinct elements of $\{0, \dots, v-1\}$ reads left to right in at least one permutation. The…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…
Let 1_k 0_l denote the (k+l)\times 1 column of k 1's above l 0's. Let q. (1_k 0_l) $ denote the (k+l)xq matrix with q copies of the column 1_k0_l. A 2-design S_{\lambda}(2,3,v) can be defined as a vx(\lambda/3)\binom{v}{2} (0,1)-matrix with…
We consider the problem of computing the data-cube marginals of a fixed order $k$ (i.e., all marginals that aggregate over $k$ dimensions), using a single round of MapReduce. The focus is on the relationship between the reducer size (number…
In this paper we investigate the spectrum of super-simple 2-$(v,5,1)$ directed designs (or simply super-simple 2-$(v,5,1)$DDs) and also the size of their smallest defining sets. We show that for all $v\equiv1,5\ ({\rm mod}\ 10)$ except…
Completely regular codes with covering radius $\rho=1$ must have minimum distance $d\leq 3$. For $d=3$, such codes are perfect and their parameters are well known. In this paper, the cases $d=1$ and $d=2$ are studied and completely…
In this paper, we consider the Reed-Muller (RM) codes. For the first order RM code, we prove that it is unique in the sense that any linear code with the same length, dimension and minimum distance must be the first order RM code; For the…
We consider when the projective special linear group over a finite field defines a $3$-design with a cyclic starter block. We will show that the equivalences of the existence of such $3$-$(q+1,5,3)$ and $3$-$(q+1,10,18)$ designs for a prime…
An $(n,k,d)$ cooperative regenerating code provides the optimal-bandwidth repair for any $t~(t\!>\!1)$ node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage…