1,025 research outputs found
Generalized Balanced Tournament Packings and Optimal Equitable Symbol Weight Codes for Power Line Communications
Generalized balance tournament packings (GBTPs) extend the concept of
generalized balanced tournament designs introduced by Lamken and Vanstone
(1989). In this paper, we establish the connection between GBTPs and a class of
codes called equitable symbol weight codes. The latter were recently
demonstrated to optimize the performance against narrowband noise in a general
coded modulation scheme for power line communications. By constructing classes
of GBTPs, we establish infinite families of optimal equitable symbol weight
codes with code lengths greater than alphabet size and whose narrowband noise
error-correcting capability to code length ratios do not diminish to zero as
the length grows
Constructions of -designs from weighing matrices and walk-regular graphs
We provide a method to construct -designs from weighing matrices and
walk-regular graphs.
One instance of our method can produce a -design from any (symmetric or
skew-symmetric) conference matrix, thereby providing a partial answer to a
question of Gunderson and Semeraro JCTB 2017.
We explore variations of our method on some matrices that satisfy certain
combinatorial restrictions.
In particular, we show that there exist various infinite families of
partially balanced incomplete block designs with block size four on the binary
Hamming schemes and the -class association schemes attached to symmetric
designs, and regular pairwise balanced designs with block sizes three and four.Comment: 31 page
Balanced semi-Latin rectangles : properties, existence and constructions for block size two
There exists a set of designs which form a subclass of semi-Latin rectangles. These designs, besides being semi-Latin rectangles, exhibit an additional property of balance; where no two distinct pairs of symbols (treatments) differ in their concurrences, that is, each pair of distinct treatments concur a constant number of times in the design. Such a design exists for a limited set of parameter combinations. We designate it a balanced semi-Latin rectangle (BSLR) and give some properties, and necessary conditions for its existence. Furthermore, algorithms for constructing the design for experimental situations where there are two treatments in each row-column intersection (block) are also given.Publisher PDFPeer reviewe
Further combinatorial constructions for optimal frequency-hopping sequences
AbstractFrequency-hopping multiple-access (FHMA) spread-spectrum communication systems employing multiple frequency shift keying as data modulation technique were investigated by Fuji-Hara, Miao and Mishima [R. Fuji-Hara, Y. Miao, M. Mishima, Optimal frequency hopping sequences: A combinatorial approach, IEEE Trans. Inform. Theory 50 (2004) 2408–2420] from a combinatorial approach, where a correspondence between frequency-hopping (FH) sequences and partition-type cyclic difference packings was established, and several combinatorial constructions were provided for FHMA systems with a single optimal FH sequence. In this paper, by means of this correspondence, we describe more combinatorial constructions for such optimal FH sequences. As a consequence, more new infinite series of optimal FH sequences are obtained
A Systematic Evaluation of Evolving Highly Nonlinear Boolean Functions in Odd Sizes
Boolean functions are mathematical objects used in diverse applications.
Different applications also have different requirements, making the research on
Boolean functions very active. In the last 30 years, evolutionary algorithms
have been shown to be a strong option for evolving Boolean functions in
different sizes and with different properties. Still, most of those works
consider similar settings and provide results that are mostly interesting from
the evolutionary algorithm's perspective. This work considers the problem of
evolving highly nonlinear Boolean functions in odd sizes. While the problem
formulation sounds simple, the problem is remarkably difficult, and the related
work is extremely scarce. We consider three solutions encodings and four
Boolean function sizes and run a detailed experimental analysis. Our results
show that the problem is challenging, and finding optimal solutions is
impossible except for the smallest tested size. However, once we added local
search to the evolutionary algorithm, we managed to find a Boolean function in
nine inputs with nonlinearity 241, which, to our knowledge, had never been
accomplished before with evolutionary algorithms.Comment: arXiv admin note: text overlap with arXiv:2311.1188
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