Related papers: How Much String to String a Cardioid?
The main aim of the note is to provide an upper-bound for the characteristic number of conic-line arrangements with ordinary singularities in the complex projective plane.
The note derives an expression for the number of interchanges made by selection sort when the sorting elements are iid variates from geometric distribution. Empirical results reveal we can work with a simpler model compared to what is…
Consider a M\"obius strip with $n$ chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can…
An n-ary k-radius sequence is a finite sequence of elements taken from an alphabet of size n such that any two distinct elements of the alphabet occur within distance k of each other somewhere in the sequence. These sequences were…
Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\rho$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger…
The interest in channel models in which the data is sent as an unordered set of binary strings has increased lately, due to emerging applications in DNA storage, among others. In this paper we analyze the minimal redundancy of binary codes…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and…
An algorithm to generate the locus of a circle using the intersection points of straight lines is proposed. The pixels on the circle are plotted independent of one another and the operations involved in finding the locus of the circle from…
Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering…
We enumerate the number of $T$-splitting subspaces of dimension $m$ for an arbitrary operator $T$ on a $2m$-dimensional vector space over a finite field. When $T$ is regular split semisimple, comparison with an alternate method of…
In this paper, we consider the problem of identifying patterns of interest in colored strings. A colored string is a string where each position is assigned one of a finite set of colors. Our task is to find substrings of the colored string…
Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a…
In this paper, we propose a general construction of linear perfect codes over infinite skew fields and quasi skew fields with right (left) unity. A complete classification of such codes over associative skew fields is given. Since the…
For a subspace arrangement over a finite field we study the evaluation code defined on the arrangement's set of points. The length of this code is given by the subspace arrangement's characteristic polynomial. For coordinate subspace…
For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none as forbidden. We examine structure of graphs whose degree sequences contain either…
Sequential lateration is a class of methods for multidimensional scaling where a suitable subset of nodes is first embedded by some method, e.g., a clique embedded by classical scaling, and then the remaining nodes are recursively embedded…
Combinatorial $t$-designs have wide applications in coding theory, cryptography, communications and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a $t$-design. In this paper, we first…