Related papers: Binary sequences with length n and nonlinear compl…
Binary machines are a generalization of Feedback Shift Registers (FSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the register stages is required. In this paper, we present an algorithm…
In this paper, we determine the linear complexity of a class of new binary cyclotomic sequences of period pn constructed by Z. Xiao et al. (Des. Codes Cryptogr. DOI 10.1007/s10623-017-0408-7) and prove their conjecture about high linear…
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
The construction of complementary sets (CSs) of sequences with different set size and sequence length become important due to its practical application for OFDM systems. Most of the constructions of CSs, based on generalized Boolean…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
Simple and efficient algorithm based on heuristic search by shotgun hill climbing to construct binary sequences with small peak sidelobe levels (PSL) is suggested. The algorithm is applied for generation of binary sequences of lengths…
In the realm of modern digital communication, cryptography, and signal processing, binary sequences with a low correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good…
We defined sufficient conditions for designing Ding-Helleseth sequences with arbitrary period and high linear complexity for generalized cyclotomies. Also we discuss the method of computing the linear complexity of Ding-Helleseth sequences…
We relate binary words with a given number of subsequences to continued fractions of rational numbers with a given denominator. We deduce that there are binary strings of length $O(\log n \log \log n)$ with exactly $n$ subsequences; this…
The main subject of the paper is everywhere complex sequences. An everywhere complex sequence is a sequence that does not contain substrings of Kolmogorov complexity less than $\alpha n-O(1)$ where $n$ is the length of substring and…
Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works…
Recently, a short and elegant proof was presented showing that a binary word of length $n$ contains at most $n-3$ runs. Here we show, using the same technique and a computer search, that the number of runs in a binary word of length $n$ is…
We show that the expected value for the linear complexity of $m$-multisequences of length $n$ is E_n^{(m)} = n m/(m+1) + O(1).
We prove the existence of a ternary sequence of factor complexity $2n+1$ for any given vector of rationally independent letter frequencies. Such sequences are constructed from an infinite product of two substitutions according to a…
We give a complete classification of binary linear complementary dual codes of lengths up to $13$ and ternary linear complementary dual codes of lengths up to $10$.
A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity…