2,440 research outputs found
Periodic Golay pairs and pairwise balanced designs
In this paper we exploit a relationship between certain pairwise balanced designs with v points and periodic Golay pairs of length v, to classify periodic Golay pairs of length less than 40. In particular, we construct all pairwise balanced designs with v points under specific block conditions having an assumed cyclic automorphism group, and using isomorph rejection which is compatible with equivalence of corresponding periodic Golay pairs, we complete a classification up to equivalence. This is done using the theory of orbit matrices and some compression techniques which apply to complementary sequences. We use similar tools to construct new periodic Golay pairs of lengths greater than 40 where classifications remain incomplete and demonstrate that under some extra conditions on its automorphism group, a periodic Golay pair of length 90 will not exist. Length 90 remains the smallest length for which existence of a periodic Golay pair is undecided. Some quasi-cyclic self-orthogonal codes are constructed as an added application
Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence
We present the results of a search of log-periodic corrections to scaling in
the moments of the energy dissipation rate in experiments at high Reynolds
number (2500) of three-dimensional fully developed turbulence. A simple
dynamical representation of the Richardson-Kolmogorov cartoon of a cascade
shows that standard averaging techniques erase by their very construction the
possible existence of log-periodic corrections to scaling associated with a
discrete hierarchy. To remedy this drawback, we introduce a novel ``canonical''
averaging that we test extensively on synthetic examples constructed to mimick
the interplay between a weak log-periodic component and rather strong
multiplicative and phase noises. Our extensive tests confirm the remarkable
observation of statistically significant log-periodic corrections to scaling,
with a prefered scaling ratio for length scales compatible with the value gamma
= 2. A strong confirmation of this result is provided by the identification of
up to 5 harmonics of the fundamental log-periodic undulations, associated with
up to 5 levels of the underlying hierarchical dynamical structure. A natural
interpretation of our results is that the Richardson-Kolmogorov mental picture
of a cascade becomes a realistic description if one allows for intermittent
births and deaths of discrete cascades at varying scales.Comment: Latex document of 40 pages, including 18 eps figure
Large Zero Autocorrelation Zone of Golay Sequences and -QAM Golay Complementary Sequences
Sequences with good correlation properties have been widely adopted in modern
communications, radar and sonar applications. In this paper, we present our new
findings on some constructions of single -ary Golay sequence and -QAM
Golay complementary sequence with a large zero autocorrelation zone, where
is an arbitrary even integer and is an arbitrary integer.
Those new results on Golay sequences and QAM Golay complementary sequences can
be explored during synchronization and detection at the receiver end and thus
improve the performance of the communication system
New Evidence of Discrete Scale Invariance in the Energy Dissipation of Three-Dimensional Turbulence: Correlation Approach and Direct Spectral Detection
We extend the analysis of [Zhou and Sornette, Physica D 165, 94-125, 2002]
showing statistically significant log-periodic corrections to scaling in the
moments of the energy dissipation rate in experiments at high Reynolds number
() of three-dimensional fully developed turbulence. First, we
develop a simple variant of the canonical averaging method using a rephasing
scheme between different samples based on pairwise correlations that confirms
Zhou and Sornette's previous results. The second analysis uses a simpler local
spectral approach and then performs averages over many local spectra. This
yields stronger evidence of the existence of underlying log-periodic
undulations, with the detection of more than 20 harmonics of a fundamental
logarithmic frequency corresponding to the preferred
scaling ratio .Comment: 9 RevTex4 papes including 8 eps figure
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