Related papers: The 2-Adic Complexity of Two Classes of Binary Seq…
Binary sequences with optimal autocorrelation play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation has been an interesting research topic in sequence design.…
A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this paper we prove that the same holds for involutions under…
All binary self-dual [44,22,8] codes with an automorphism of order 3 or 7 are classified. In this way we complete the classification of extremal self-dual codes of length 44 having an automorphism of odd prime order.
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly $2272$ noncorrelated binary pattern sequences of length $\leq 4$. If we restrict our…
The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…
We study the complexity of reasoning in abstracts argumentation frameworks close to graph classes that allow for efficient reasoning methods, i.e.\ to one of the classes of acyclic, noeven, biparite and symmetric AFs. In this work we show…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…
As a continuation of the authors and Wakatsuki's previous paper [5], we study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms. We show that for any integral models of the space of binary cubic…
We consider the learning and communication complexity of subsequence containment. In the learning problem, we seek to learn a classifier that positively labels a binary string $x$ if it contains a fixed binary string $y$ as a subsequence.…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
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…
A graph G is a 2-tree if G=K_3, or G has a vertex v of degree 2, whose neighbours are adjacent, and G\v{i}s a 2-tree. A characterization of the degree sequences of 2-trees is given. This characterization yields a linear-time algorithm for…
In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular…
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…
The merit factor of a $\{-1, 1\}$ binary sequence measures the collective smallness of its non-trivial aperiodic autocorrelations. Binary sequences with large merit factor are important in digital communications because they allow the…