Related papers: Low Autocorrelation Binary Sequences: Number Theor…
The search for binary sequences with a high figure of merit, known as the low autocorrelation binary sequence ($labs$}) problem, represents a formidable computational challenge. To mitigate the computational constraints of the problem, we…
A Barker sequence is a binary sequence for which all nontrivial aperiodic autocorrelations are either 0, 1 or -1. The only known Barker sequences have length 2, 3, 4, 5, 7, 11 or 13. It is an old conjecture that no longer Barker sequences…
In this paper, we present a computational search for best-known merit factors of longer binary sequences with an odd length. Finding low autocorrelation binary sequences with optimal or suboptimal merit factors is a very difficult…
The interplay between the ground state energy of the generalized Bernasconi model to multi-phase, and the minimal value of the maximal autocorrelation function, $C_{max}=\max_K{|C_K|}$, $K=1,..N-1$, is examined analytically and the main…
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation…
Certain applications require the use of signals that combine both the capability to operate with low signal-to-noise ratios and the ability to support multiple users without interference. In the case where many users have very different…
Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the…
Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a…
Various problems in engineering and natural science demand binary sequences that do not resemble translates of themselves, that is, the sequences must have small aperiodic autocorrelation at every nonzero shift. If $f$ is a sequence, then…
Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at…
Low correlation (finite length) sequences are used in communications and remote sensing. One seeks codebooks of sequences in which each sequence has low aperiodic autocorrelation at all nonzero shifts, and each pair of distinct sequences…
The identification of binary sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications…
The run vector of a binary sequence reflects the run structure of the sequence, which is given by the set of all substrings of the run length encoding. The run vector and the aperiodic autocorrelations of a binary sequence are strongly…
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…
The search of binary sequences with low auto-correlations (LABS) is a discrete combinatorial optimization problem contained in the NP-hard computational complexity class. We study this problem using Warning Propagation (WP) , a message…
Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For…
The merit factor problem is of practical importance to manifold domains, such as digital communications engineering, radars, system modulation, system testing, information theory, physics, chemistry. However, the merit factor problem is…
A Barker sequence is a binary sequence for which all nontrivial aperiodic autocorrelations are at most 1 in magnitude. An old conjecture due to Turyn asserts that there is no Barker sequence of length greater than 13. In 1961, Turyn and…
Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such…
Sequences with low aperiodic autocorrelation are used in communications and remote sensing for synchronization and ranging. The autocorrelation demerit factor of a sequence is the sum of the squared magnitudes of its autocorrelation values…