We introduce notions of local and interweight spectra of an arbitrary coloring of a Boolean cube, which generalize the notion of a weight spectrum. The main objects of our research are colorings that are called perfec...
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We introduce notions of local and interweight spectra of an arbitrary coloring of a Boolean cube, which generalize the notion of a weight spectrum. The main objects of our research are colorings that are called perfect. We establish an interrelation of local spectra of such a coloring in two orthogonal faces of a Boolean cube and study properties of the interweight spectrum. Based on this, we prove a new metric property of perfect colorings, namely, their strong distance invariance. As a consequence, we obtain an analogous property of an arbitrary completely regular code, which, together with his neighborhoods, forms a perfect coloring.
Bent functions are maximally nonlinear Boolean functions. Introduced by Rothaus and first examined by Dillon, these important functions have subsequently been studied by many researchers over the last four decades. Si...
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Bent functions are maximally nonlinear Boolean functions. Introduced by Rothaus and first examined by Dillon, these important functions have subsequently been studied by many researchers over the last four decades. Since a complete classification of bent functions appears elusive, many researchers concentrate on methods for constructing bent functions. In this paper, we investigate constructions of bent functions from involutions over finite fields in even characteristic. We present a generic construction technique, study its equivalence issues and show that linear involutions (which are an important class of permutations) over finite fields give rise to bent functions in bivariate representations. In particular, we exhibit new constructions of bent functions involving binomial linear involutions, whose dual functions are directly obtained without computation. The existence of bent functions from involutions relies heavily on solving systems of equations over finite fields.
Flash memory is a nonvolatile computer memory comprising blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomp...
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Flash memory is a nonvolatile computer memory comprising blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomplished only by erasing an entire block. Since block erasures are highly undesirable, coding schemes-known as floating codes (or flash codes) and buffer codes-have been designed in order to maximize the number of times that information stored in a flash memory can be written (and rewritten) prior to incurring a block erasure. An (n, k, t)(q) flash code C is a coding scheme for storing k information bits in n cells in such a way that any sequence of up to t writes can be accommodated without a block erasure. The total number of available level transitions in n cells is n(q-1), and the write deficiency of C, defined as delta(C) = n(q-1) - t, is a measure of how close the code comes to perfectly utilizing all these transitions. In this paper, we show a construction of flash codes with write deficiency O(qk log k) if q >= log(2) k, and at most O(k log(2) k) otherwise. An (n, r, l, t) q buffer code is a coding scheme for storing a buffer of r l-ary symbols such that for any sequence of t symbols, it is possible to successfully decode the last r symbols that were written. We improve upon a previous upper bound on the maximum number of writes t in the case where there is a single cell to store the buffer. Then, we show how to improve a construction by Jiang et al. that uses multiple cells, where n >= 2r.
This paper presents an overview of the coding aspects of a GNSS receiver. coding allows detection and correction of channel-induced errors at the receiver, here the focus is on the mitigation of threats from malicious...
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This paper presents an overview of the coding aspects of a GNSS receiver. coding allows detection and correction of channel-induced errors at the receiver, here the focus is on the mitigation of threats from malicious interferences. Although the effects of interference at different stages of GNSS baseband processing has been deeply analyzed in the literature, little attention was devoted to its impact on the navigation message decoding stage. Theis paper provides an introduction to the various coding schemes employed by current GNSS signals, discussing their performance in the presence of noise in terms of block-error rate. Additionally, the benefits of soft-decoding schemes for navigation message decoding are highlighted when jamming interferences are present. The proposed scheme requires estimating the noise plus interference power, yielding to enhanced decoding performances under severe jamming conditions. Finally, cryptographic schemes as a means of providing anti-spoofing for geosecurity location-based services, and their potential vulnerability are discussed, with particular emphasis on the dependence on the dependence of the scheme on successful navigation message decoding.
The concept of entropy has played a significant role in thermodynamics and information theory, and is also a current research hotspot. Information entropy, as a measure of information, has many different forms, such a...
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The concept of entropy has played a significant role in thermodynamics and information theory, and is also a current research hotspot. Information entropy, as a measure of information, has many different forms, such as Shannon entropy and Deng entropy, but there is no unified interpretation of information from a measurement perspective. To address this issue, this article proposes Generalized Information Entropy (GIE) that unifies entropies based on mass function. Meanwhile, GIE establishes the relationship between entropy, fractal dimension, and number of events. Therefore, Generalized Information Dimension (GID) has been proposed, which extends the definition of information dimension from probability to mass fusion. GIE plays a role in approximation calculation and coding systems. In the application of coding, information from the perspective of GIE exhibits a certain degree of particle nature that the same event can have different representational states, similar to the number of microscopic states in Boltzmann entropy.
The software for portable systems for obtaining. image with coding apertures (masks) is described. The software developed controls all systems that form an image and obtain shadow patterns, reconstructs the initial ga...
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The software for portable systems for obtaining. image with coding apertures (masks) is described. The software developed controls all systems that form an image and obtain shadow patterns, reconstructs the initial gamma-image, and processes previously obtained images. The software is used with portable systems in which URA and MURA type masks with different rank are used as the coding aperture. Programs for modeling the process of obtaining shadow patterns using real apparatus which has different position-sensitive detectors are described. Possible configurations of new apparatus which could be of practical interest are examined.
This study investigates the effect of multiple sources using STS across a Time-Hopping-PPM Modulation that is over an UWB Saleh-Valenzuela channel with each source using two transmit antennas. We model and analyze thi...
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This study investigates the effect of multiple sources using STS across a Time-Hopping-PPM Modulation that is over an UWB Saleh-Valenzuela channel with each source using two transmit antennas. We model and analyze this system, showing that the presence of such MAI results in a significant degradation in BER performance. Simulation results show that for strong signal strength of interfering MAI signals degradation in BER performance is observed for the cases where we have five and 10 distinct MAI sources present when using Walsh-Hadamard thirty two chip spreading sequences. Using simulation, we investigate the use of other sets of orthogonal spreading sequences with improved cross correlation properties and find that for some sequences a significant improvement is seen compared to Walsh-Hadamard sequences when they are similarly misaligned. We show that MAI degrades the BER performance of such systems and that selection of improved cross correlation spreading code sequence sets improves BER. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.
We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic ...
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We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group algebra of a nilpotent group. (C) 2010 Elsevier Inc. All rights reserved.
We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability epsilon. We analyze the minimal ov...
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We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability epsilon. We analyze the minimal overhead that must be added by the coding scheme to succeed in performing the computation despite the noise. Our main result is a lower bound on the communication of any noise-resilient protocol over a synchronous star network with n parties (where all parties communicate in every round). Specifically, we show a task that can be solved by communicating T bits over the noise-free network, but for which any protocol with success probability of 1 - o(1) must communicate at least Omega(T log n/log log n) bits when the channels are noisy. By a 1994 result of Rajagopalan and Schulman, the slowdown we prove is the highest one can obtain on any topology, up to a log log n factor. We complete our lower bound with a matching coding scheme that achieves the same overhead;thus, the capacity of (synchronous) star networks is Theta(log log n/log n). Our bounds prove that, despite several previous coding schemes with rate Omega(1) for certain topologies, no coding scheme with constant rate Omega(1) exists for arbitrary n-party noisy networks.
In this paper, we give an explicit construction of a family of capacity-achieving binary t-write WOM codes for any number of writes t, which have polynomial time encoding and decoding algorithms. The block length of o...
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In this paper, we give an explicit construction of a family of capacity-achieving binary t-write WOM codes for any number of writes t, which have polynomial time encoding and decoding algorithms. The block length of our construction is N = (t/epsilon)(O(t/(delta epsilon))) when epsilon is the gap to capacity and encoding and decoding run in time N1+ delta. This is the first deterministic construction achieving these parameters. Our techniques also apply to larger alphabets.
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