The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Diego Napp - One of the best experts on this subject based on the ideXlab platform.
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Systematic maximum sum rank codes
Finite Fields and Their Applications, 2020Co-Authors: Paulo José Fernandes Almeida, Umberto Martínez-peñas, Diego NappAbstract:Abstract In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This work follows this thread of research and studies the characterization of Systematic generator matrices (encoders) of codes with maximum rank distance. In the context of Hamming distance these codes are the so-called Maximum Distance Separable (MDS) codes and Systematic encoders have been fully investigated. In this paper we investigate the algebraic properties and representation of encoders in Systematic Form of Maximum Rank Distance (MRD) codes and Maximum Sum Rank Distance (MSRD) codes. We address both block codes and convolutional codes separately and present necessary and sufficient conditions for an encoder in Systematic Form to generate a code with maximum (sum) rank distance. These characterizations are given in terms of certain matrices that must be superregular in a extension field and that preserve superregularity after some transFormations perFormed over the base field. We conclude the work presenting some examples of Maximum Sum Rank convolutional codes over small fields. For the given parameters the examples obtained are over smaller fields than the examples obtained by other authors.
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Generalized Column Distances
IEEE Transactions on Information Theory, 2020Co-Authors: Sara D. Cardell, Marcelo Firer, Diego NappAbstract:The notion of Generalized Hamming weights of block codes has been investigated since the nineties due to its significant role in coding theory and cryptography. In this paper we extend this concept to the context of convolutional codes. In particular, we focus on column distances and introduce the novel notion of generalized column distances (GCD). We first show that the hierarchy of GCD is strictly increasing. We then provide characterizations of such distances in terms of the truncated parity-check matrix of the code, that will allow us to determine their values. Finally, the case in which the parity-check matrix is in Systematic Form is treated.
G. Robert Redinbo - One of the best experts on this subject based on the ideXlab platform.
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Systematic Wavelet Codes: Designed and Decoded by DFT Vectors
IEEE Transactions on Communications, 2018Co-Authors: G. Robert RedinboAbstract:A class of complex-valued convolutional codes, wavelet codes, that encode numbers into numbers, is constructed by assigning consecutively indexed discrete Fourier transForm (DFT) vectors to the parity-checking requirements. For a rate $k/n$ code with constraint length $m$ , the parameters must satisfy (m + 1)(n-k) $m$ , the errors can be corrected by extracting from the convolutional code’s syndromes, new syndromes associated with a DFT block code inherent in the code’s algebraic structure. A modified Berlekamp–Massey algorithm computes the error locations and the correcting values are determined by an inverse DFT operation. Systematic Forms of these codes are developed by manipulating the original generating transfer function. Each Systematic Form is a subcode of the original wavelet code from which it was determined. Moreover, this Form may be decoded by DFT code methods too. Extensive simulation results verify the power and viability of both Forms of the codes and their decoding techniques.
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Systematic Wavelet Subcodes for Data Protection
IEEE Transactions on Computers, 2011Co-Authors: G. Robert RedinboAbstract:Real number data processing failures are detected by comparing parity values associated with a wavelet code which is most efficient in Systematic Form. Any rate k/n wavelet code, a Form of real number convolutional code, is manipulated into a Systematic wavelet subcode, with slightly reduced rate (k-1)/n, staying within the original algebraic structure.
Napp Diego - One of the best experts on this subject based on the ideXlab platform.
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Generalized Column Distances
'Institute of Electrical and Electronics Engineers (IEEE)', 2021Co-Authors: Cardell, Sara D., Firer Marcelo, Napp DiegoAbstract:The notion of Generalized Hamming weights of block codes has been investigated since the nineties due to its significant role in coding theory and cryptography. In this paper we extend this concept to the context of convolutional codes. In particular, we focus on column distances and introduce the novel notion of generalized column distances (GCD). We first show that the hierarchy of GCD is strictly increasing. We then provide characterizations of such distances in terms of the truncated parity-check matrix of the code, that will allow us to determine their values. Finally, the case in which the parity-check matrix is in Systematic Form is treated.This work was supported in part by the Sao Paulo Research Foundation (FAPESP) under Grant 2013/25977-7. The work of Sara D. Cardell was supported in part by the FAPESP, under Grant 2015/07246-0 and in part by the CAPES. The work of Marcelo Firer was supported in part by the CNPq. The work of Diego Napp was supported in part by the Spanish, Generalitat Valenciana, Univesitat d’Alacant, under Grant AICO/2017/128 and Grant VIGROB-287
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Systematic maximum sum rank codes
'Elsevier BV', 2020Co-Authors: Almeida Paulo, Martínez-peñas Umberto, Napp DiegoAbstract:In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This work follows this thread of research and studies the characterization of Systematic generator matrices (encoders) of codes with maximum rank distance. In the context of Hamming distance these codes are the so-called Maximum Distance Separable (MDS) codes and Systematic encoders have been fully investigated. In this paper we investigate the algebraic properties and representation of encoders in Systematic Form of Maximum Rank Distance (MRD) codes and Maximum Sum Rank Distance (MSRD) codes. We address both block codes and convolutional codes separately and present necessary and sufficient conditions for an encoder in Systematic Form to generate a code with maximum (sum) rank distance. These characterizations are given in terms of certain matrices that must be superregular in a extension field and that preserve superregularity after some transFormations perFormed over the base field. We conclude the work presenting some examples of Maximum Sum Rank convolutional codes over small fields. For the given parameters the examples obtained are over smaller fields than the examples obtained by other authors.publishe
Jack Spencer - One of the best experts on this subject based on the ideXlab platform.
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Rational monism and rational pluralism
Philosophical Studies, 2020Co-Authors: Jack SpencerAbstract:Consequentialists often assume rational monism: the thesis that options are always made rationally permissible by the maximization of the selfsame quantity. This essay argues that consequentialists should reject rational monism and instead accept rational pluralism: the thesis that, on different occasions, options are made rationally permissible by the maximization of different quantities. The essay then develops a Systematic Form of rational pluralism which, unlike its rivals, is capable of handling both the Newcomb problems that challenge evidential decision theory and the unstable problems that challenge causal decision theory.
François Lévy - One of the best experts on this subject based on the ideXlab platform.
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CNL - Towards a High-Level Controlled Language for Legal Sources on the Semantic Web
Lecture Notes in Computer Science, 2016Co-Authors: Adam Wyner, Adeline Nazarenko, François LévyAbstract:Legislation and regulations are required to be structured and augmented in order to make them serviceable on the Internet. However, it is known that it is complex to accurately parse and semantically represent such texts. Controlled languages have been one approach to adjusting to the complexities, where the source text is rewritten in some Systematic Form. Such an approach is not only costly, but potentially introduces alternative translations which may be undesirable. To navigate between the requirements and complexities, we propose and exemplify a high-level controlled language that serves as an XML representation for key components of legal content. The language tightly correlates to the source text and also facilitates analysis.
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Towards a High-level Controlled Language for Legal Sources on the Semantic Web
2015Co-Authors: François Lévy, Adeline Nazarenko, Adam WynerAbstract:Legislation and regulations are required to be structured and augmented in order to make them serviceable on the Internet. However, it is known that it is complex to accurately parse and semantically represent such texts. Controlled languages have been one approach to adjusting to the complexities, where the source text is rewritten in some Systematic Form. Such an approach is not only costly, but potentially introduces alternative translations which may be undesirable. To navigate between the requirements and complexities, we propose and exemplify a high- level controlled language that serves as a high level XML representation for key components of legal content. The language tightly correlates to the source text and also facilitates analysis.
