## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Foundations of Data Science
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

AMC

We apply combinatorial arguments to establish structural constraints on Costas arrays. We prove restrictions on when a Costas array can
contain a large corner region whose entries are all 0. In particular, we prove
a 2010 conjecture due to Russo, Erickson and Beard. We then constrain the
vectors joining pairs of 1s in a Costas array by establishing a series of results
on its number of "mirror pairs," namely pairs of these vectors having the same
length but opposite slopes.

keywords:
Costas array
,
mirror pair
,
structural constraints.
,
common vector
,
all-zero corner region

AMC

The peak sidelobe level (PSL) of a binary sequence is the largest absolute value of all its nontrivial aperiodic autocorrelations. A classical problem of digital sequence design is to determine how slowly the PSL of a length $n$
binary sequence can grow, as $n$ becomes large. Moon and Moser showed in 1968 that the growth rate of the PSL of almost all length $n$ binary sequences lies between order $\sqrt{n\log n}$ and $\sqrt{n}$, but since then no theoretical improvement to
these bounds has been found.

We present the first numerical evidence on the tightness of these bounds, showing that the PSL of almost all binary sequences of length $n$ appears to grow exactly like order $\sqrt{n\log n}$, and that the PSL of almost all $m$-sequences of length $n$ appears to grow exactly like order $\sqrt{n}$. In the case of $m$-sequences, a key algorithmic insight reveals behaviour that was previously well beyond the range of computation.

We present the first numerical evidence on the tightness of these bounds, showing that the PSL of almost all binary sequences of length $n$ appears to grow exactly like order $\sqrt{n\log n}$, and that the PSL of almost all $m$-sequences of length $n$ appears to grow exactly like order $\sqrt{n}$. In the case of $m$-sequences, a key algorithmic insight reveals behaviour that was previously well beyond the range of computation.

AMC

We calculate the asymptotic merit factor, under all rotations of
sequence elements, of two families of binary sequences derived from Legendre sequences. The rotation is negaperiodic for the first family, and periodic for the second family. In both cases the maximum asymptotic merit factor is 6. As a consequence, we obtain the first two families of skew-symmetric sequences with known asymptotic merit factor, which is also 6 in both cases.

keywords:
skew-symmetric.
,
negaperiodic
,
construction
,
asymptotic
,
merit factor
,
rotation
,
Legendre sequence
,
periodic
,
Binary sequence

## Year of publication

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