Related papers: A Construction for Balancing Non-Binary Sequences …
Binary code analysis allows analyzing binary code without having access to the corresponding source code. A binary, after disassembly, is expressed in an assembly language. This inspires us to approach binary analysis by leveraging ideas…
Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two…
Sentence ordering aims at arranging a list of sentences in the correct order. Based on the observation that sentence order at different distances may rely on different types of information, we devise a new approach based on multi-granular…
Each positive increasing integer sequence $\{a_n\}_{n\geq 0}$ can serve as a numeration system to represent each non-negative integer by means of suitable coefficient strings. We analyse the case of $k$-generalized Fibonacci sequences…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
A critical challenge for any intelligent system is to infer structure from continuous data streams. Theories of event-predictive cognition suggest that the brain segments sensorimotor information into compact event encodings, which are used…
We provide a trace partitioned Gray code for the set of q-ary strings avoiding a pattern constituted by k consecutive equal symbols. The definition of this Gray code is based on two different constructions, according to the parity of q.…
The article is devoted to a matrix method of comparative analysis of long nucleotide sequences by means of a presentation of each sequence in a form of three digital binary sequences. This method uses biochemical attributes of nucleotides…
This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…
Conventional unsupervised hashing methods usually take advantage of similarity graphs, which are either pre-computed in the high-dimensional space or obtained from random anchor points. On the one hand, existing methods uncouple the…
An approach based on the kernel methods for capturing the nonlinear interdependence between two signals is introduced. It is demonstrated that the proposed approach is useful for characterizing generalized synchronization with a successful…
We revisit hierarchical bracketing encodings from a practical perspective in the context of dependency graph parsing. The approach encodes graphs as sequences, enabling linear-time parsing with $n$ tagging actions, and still representing…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We consider the problem of compressing memoryless binary data with or without side information at the decoder. We review the parity- and the syndrome-based approaches and discuss their theoretical limits, assuming that there exists a…
A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal…
We study the problem of compressing a source sequence in the presence of side-information that is related to the source via insertions, deletions and substitutions. We propose a simple algorithm to compress the source sequence when the…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…
We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi kernel polar…
This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a…
We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when…