Related papers: Sidon Sequences and Doubly Periodic Two-Dimensiona…
The flow of contracting systems contracts 1-dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting…
We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the first main result by H. Xiong, L. Qu, and C. Li, IEEE Transactions on Information…
The construction of self-dual codes over small fields such that their minimum distances are as large as possible is a long-standing challenging problem in the coding theory. In 2009, a family of binary self-dual cyclic codes with lengths…
Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of $q$-ary projective two-weight linear codes is presented, where $q$ is a power of 2. The parameters of…
The correspondence between perfect difference sets and transitive projective planes is well-known. We observe that all known dense (i.e., close to square-root size) Sidon subsets of abelian groups come from projective planes through a…
Universally decodable matrices can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $n$ and a prime power $q$. Based on Pascal's triangle we give an…
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…
Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the…
The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, data can be fitted as low-order polynomials of the 6…
A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a…
This paper is a short survey of the recent results on examples of periodic two-dimensional continued fractions (in Klein's model). In the last part of this paper we formulate some questions, problems and conjectures on geometrical…
The ability to generate natural language sequences from source code snippets has a variety of applications such as code summarization, documentation, and retrieval. Sequence-to-sequence (seq2seq) models, adopted from neural machine…
We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.
When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…
The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…
We use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group $S_n$ in order to construct recurrence relations for enumerating certain subsets of $S_n$. Occasionally one can find `closed form'…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
The manuscript describes fast and scalable architectures and associated algorithms for computing convolutions and cross-correlations. The basic idea is to map 2D convolutions and cross-correlations to a collection of 1D convolutions and…